What is the purpose of performing a test cross?

To determine the precise genotype of an organism.

Since dominant alleles are displayed with only 1 allele present, it can be impossible to tell the difference between a homozygous dominant gene and a heterozygous gene, as they have the same phenotype.

However, if you cross it with a homozygous recessive gene, if it makes any recessive genes, then it was heterozygous. If, after many tests, it does not make any recessive genes, then it was homozygous dominant. This is because the homozygous dominant gene will "give" 1 dominant allele to each new gene, making them all dominant.

This process is called a test cross, since you are testing the exact genotype of an organism to see if it is heterozygous or homozygous dominant.