The application of computer technology to the management of biological information. Specifically, it is the science of developing computer databases and algorithms to facilitate and expedite biological research, particularly in genomics.

Bioinformatics is an emerging discipline, which combines efforts and advances in computer science, computational science, and various aspects of life science. While there is currently no generally agreed upon definition of 'bioinformatics,' one view is that bioinformatics is concerned with the creation and development of advanced information and computational technologies to solve problems in biology. That is, bioinformatics typically relies on techniques from informatics, involving efficient algorithms for manipulating large amounts of data stored and processed on high-performance computers, in order to obtain information about genomic or protein sequence data. Bioinformatics is often applied to problems in computational chemistry, functional genomics, neural imaging (brain mapping), pharmacogenetics, pharmacogenomics, pharmacometrics, proteomics, and structural biology.

A staple of bioinformatics is the creation and maintenance of databases of biological information. However, due to the success of the human genome project a more immediate and pressing task requires the analysis of sequence information. This field of computational biology typically involves finding the genes in the DNA sequences of various organisms, developing methods to predict the structure and/or function of sequences, clustering protein sequences into families of related sequences, and aligning similar proteins in order to evaluate evolutionary relationships.

Bioinformatics derives knowledge from computer analysis of biological data. These can consist of the information stored in the genetic code, but also experimental results from various sources, patient statistics, and scientific literature. Research in bioinformatics includes method development for storage, retrieval, and analysis of the data. Bioinformatics is a rapidly developing branch of biology and is highly interdisciplinary, using techniques and concepts from informatics, statistics, mathematics, chemistry, biochemistry, physics, and linguistics. It has many practical applications in different areas of biology and medicine.

Bioinformatics: The science of developing computer databases and algorithms for the purpose of speeding up and enhancing biological research. Bioinformatics is being used most noticeably in the Human Genome Project, the effort to identify the 80,000 genes in human DNA . New academic programs are training students in Bioinformatics by providing them with backgrounds in molecular biology and in computer science, including database design and analytical approaches.

Here some more definition of Bioinformatics pulled from Web

1.Bioinformatics: The use of computers in solving information problems in the life sciences, mainly, it involves the creation of extensive electronic databases on genomes, protein sequences, etc. Secondarily, it involves techniques such as the three-dimensional modeling of biomolecules and biologic systems. 
Cancer Web

2.What is Bioinformatics? Bioinformatics is an integration of mathematical, statistical and computer methods to analyze biological, biochemical and biophysical data. 
(Georgia Tech)

3.Bioinformatics: The science of developing computer databases and algorithms for the purpose of speeding up and enhancing biological research. Bioinformatics is being used most noticeably in the Human Genome Project, the effort to identify the 80,000 genes in human DNA . New academic programs are training students in Bioinformatics by providing them with backgrounds in molecular biology and in computer science, including database design and analytical approaches. 
(whatis.com)

4.What is Bioinformatics? The definition of bioinformatics is not univerally agreed upon. Generally speaking, we define it as the creation and development of advanced information and computational technologies for problems in biology, most commonly molecular biology (but increasingly in other areas of biology). As such, it deals with methods for storing, retrieving and analyzing biological data, such as nucleic acid (DNA/RNA) and protein sequences, structures, functions, pathways and genetic interactions. 
Some people construe bioinformatics more narrowly, and include only those issues dealing with the management of genome project sequencing data. Others construe bioinformatics more broadly and include all areas of computational biology, including population modeling and numerical simulations. 
(Stanford University)

5.Bioinformatics can be defined as the storage, manipulation and analysis of biological information via computer science. Bioinformatics is an essential infrastructure underpinning biological research. 
(Roslin Institute)

6.Definition: What is Bioinformatics? Bioinformatics is the study of the inherent structure of biological information and biological systems. It brings together the avalanche of systematic biological data (e.g. genomes) with the analytic theory and practical tools of computer science and mathematics. 
The complex and richly structured data from genomics can be viewed as the greatest encoding problem of all time (e.g. genome ® organism). From this perspective, the sequencing of the human and other genomes can be viewed as one of the all-time great opportunities for theorists interested in information, its structure and analysis. This formulation of the "bioinformatics problem" opens the way for biologists to collaborate with mathematicians and computer scientists, because it aims to translate "biology problems" into new challenges that are interesting to theoreticians--problems of information content, structure and encoding, which inherently interest theorists. By contrast, the common view (and practice) of bioinformatics, as simply an application of existing mathematical or CS tools to biological problems, has little fundamental interest as a research program for mathematicians and computer scientists.

As we have defined it, bioinformatics is the analysis and interpretation of genomics data; i.e. genomics generates data, and bioinformatics provides analytical tools enabling interpretation of those data. Thus, the underlying dynamic (repeated over and over in specific examples--mapping, sequences, expression data, etc.) is the drive from data to understanding, abstracting from specific, concrete biological data analysis problems to the underlying theoretical problems of elucidating, representing, and analyzing the inherent structure within the biological information. This translates biological questions ("I want to find the orthologs of these genes.") into the language of information content, structure and encoding, to bring in the mathematics and computer science needed to solve these problems.

Thus, in place of a grab-bag program (which one might represent by a variety of topics randomly distributed over a field, with sparse inter-connections), our vision is of a star topology (illustrated below), in which the definition of bioinformatics acts as the center connecting the data (microcosm) to the underlying theoretical problems of elucidating the structure of that information. 
(UCLA)

7.Definition: Bioinformatics derives knowledge from computer analysis of biological data. These can consist of the information stored in the genetic code, but also experimental results from various sources, patient statistics, and scientific literature. Research in bioinformatics includes method development for storage, retrieval, and analysis of the data. Bioinformatics is a rapidly developing branch of biology and is highly interdisciplinary, using techniques and concepts from informatics, statistics, mathematics, chemistry, biochemistry, physics, and linguistics. It has many practical applications in different areas of biology and medicine. 
(Pasteur Institute)

8.What is bioinformatics? Bioinformatics is the application of computer technology to the management of biological information. Computers are used to gather, store, analyze and integrate biological and genetic information which can then be applied to gene-based drug discovery and development. The need for Bioinformatics capabilities has been precipitated by the explosion of publicly available genomic information resulting from the Human Genome Project. The goal of this project - determination of the sequence of the entire human genome (approximately three billion base pairs) - will be reached by the year 2002. The science of Bioinformatics, which is the melding of molecular biology with computer science, is essential to the use of genomic information in understanding human diseases and in the identification of new molecular targets for drug discovery. In recognition of this, many universities, government institutions and pharmaceutical firms have formed bioinformatics groups, consisting of computational biologists and bioinformatics computer scientists. Such groups will be key to unraveling the mass of information generated by large scale sequencing efforts underway in laboratories around the world. (BioPlanet)

9.Bioinformatics is a recently established field of science drawing data from the traditional field of biology, but also ancillary data from sources including agriculture, atmospheric and soil science, medicine, and economics. The traditional definition of bioinformatics is "the systematic development and application of computing systems and computational solution techniques analyzing data obtained by experiments, modeling, database search, and instrumentation regarding biological aspects." To date, this definition, the activities described, and job opportunities have been primarily in the fields of molecular genetics, genomic projects, and pharmaceuticals. We have broadened and extended the definition of bioinformatics to include "the delivery of the data and its synthesis to decision makers and potential users, including the general public." 
(Texas Tech)

10.Bioinformatics:The application of computer technology to the management of biological information. Specifically, it is the science of developing computer databases and algorithms to facilitate and expedite biological research. Bioinformatics is being used largely in the field of human genome research by the Human Genome Project that has been determining the sequence of the entire human genome (about 3 billion base pairs) and is essential in using genomic information to understand diseases. It is also used largely for the identification of new molecular targets for drug discovery. 
(webopedia)