Homozygous. In the case of Showgirls, it means a bird genetically pure for the naked neck gene.
Which means if you breed a homozygous roo to pure silkie hens, all of the chicks will be showgirls(naked necks). The chicks won't be homozygous though.
BTW the term for not genetically pure for a trait is called Heterozygous. As in:
Heterozygous roo bred to silkie hens: Half showgirl and half silkie chicks.
edited to add, for the naked neck gene it does not matter which parent has it. Above was only an example- silkie rooster over showgirl hen would give same results..
Birds that are homozygous for the naked neck gene do not have the bow-tie in the center front of neck. Their necks are totally naked or may have only a couple feathers in the front center.
Homozygous - 2 genes
So the Showgirl has 2 naked neck genes, thus all of this birds offspring will get 1 gene from this bird there for be naked necked.
heterozygous- 1 gene
from a showgirl with only 1 nn gene only 50% of its offspring will inherit the nn gene. So crossed with a non-nn bird only 50% of chicks will be nn, but if crossed with a homozygous you get 50% homozygous nn and 50% heterozygous nn chicks, and if crossed with another heterozygous you would get 25% homozygous nn, 25% w/o nn gene and 50% heterozygous nn.