A crossing of a creature with its parents to find out which allele of a gene it has. This is a technique that can be used to purify one strain by only keeping the desired genetic property.
If a gene has two alleles, G and g, and G is dominant over the g, then the two genotypes GG (homozygous) and Gg (heterozygous) will both come out looking the same: they will have the phenotype of the dominant G. To find out which they have, you mate them with creatures of known genotype gg.
If your test organism is Gg then a proportion of their offspring will inherit the recessive g from both parents and appear as phenotypically gg.
The dominance may be so clear-cut that a single backcross can decide it, e.g. normal coat colour versus albino. Here there are no intermediates. But with most genes the presence of the gene being sought is not so clear cut, so several generations of backcrossing may be used to increase the probability that the strain now contains the pure allele. A genotype GG mated with gg never produces gg offspring, but this might also happen by chance if its genotype was Gg: repeated backcrossing reduces the possibility of this.
A backcross is also known as a testcross. To get the same genetic effect, the mating does not actually have to be with a parent: e.g. any albino clearly has a known genotype, and would work as well.