If you're homozygous, you’ve got a pair of matching alleles, which are the two genes that control a particular trait. If both your alleles that determine blood type are O, you're homozygous — and you've got type O blood.
The Greek root homo- means "same," and a zygote is a cell created when two gametes — a sperm and an egg, in humans — come together. The zygote gets half its genetic material from each parent, one allele in the pair from each. If the eye color allele you inherit from your mother and the one you get from your father are both for blue eyes, then you’re homozygous for that trait (and you have blue eyes).