Two DNA or RNA sequences are said to be 'homologous' when they are almost the same.
Homologous recombination is a biological event that happens during cell replication that increases the genetic variability of offspring. Homologous regions of DNA are allowed to mix among chromosomes, creating 'new' chromosomes in the replicated cells. This is a very complex process that only happens while cells are dividing.
Homologous recombination is used in knockout methods by creating a sequence of DNA that is similar to the target, but different enough to create a change in the genome. This DNA is then put into the cells and the cells allowed to replicate. During the homologous recombination stage some of the altered sequence is inserted into the genome by the homologous recombination machinery, resulting in an altered cell line. The new cells are then screened to find the ones that have the mutation.