Gene duplication occurs when an error in DNA replication leads to the duplication of a region of DNA containing a (generally functional) gene. The significance of this process for evolutionary biology is that if a gene is under natural selection, most mutations will lead to the death of the organism. When a gene is duplicated selection may be removed from one copy and now the other gene locus is free to mutate and discover new functions. Alternatively, the gene may acquire deleterious mutations and become a pseudogene.
The postulate that gene duplication has a major role in evolution was developed in the 1980s and is now widely accepted as a major evolutionary force. Some have argued that gene duplication is the most important evolutionary force since the emergence of the universal common ancestor.
Major genome duplication events are not uncommon. It is predicted that the entire yeast genome underwent duplication only ~1,000,000 years ago. Plants are the most prolific genome duplicators. Wheat for example is hexaploid (a specific term for a polyploid organism) meaning it has six duplicate copies of its genome.
The two genes that exists after a gene duplication event are paralogs. Paralogs usually code for proteins with different function and/or structure as stated above. This is opposed to orthologous genes that code for proteins with similar function but that exists in different species. Orthologs are created from a speciation event. (See Homology of sequences in genetics)
It is important (but often hard) to differentiate between paralogs and orthologs in biological research. Experiments on human gene function can often be carried out on other species if a homolog to a human gene can be found in the genome of that species. But only if the homolog is orthologous. If they are paralogs and resulted from a gene duplication event their function is probably too different.