Hybrid plants are a cross between two different varieties. Hybrid vigor describes the way first generation hybrid plants often perform better than either parent.
How is this possible?
The answer lies in genetics. Most species, including humans, carry some defective genes, but when there's a second, "good" copy of the same gene, the good copy activates instead. First generation hybrid plants inherit different sets of genes from each parent, so they're more likely to have at least one good copy of each gene. However, things get tricky when vigorous, first generation hybrids produce offspring. Let's say you planted a delicious hybrid tomato in your garden and want to grow it again next year. Can you simply save the tomato's seeds?
Sprouting seeds from your hybrid tomato is like rolling a pair of genetic dice. Only half of a first generation hybrid's genes influence its development, so its seedling could develop bad characteristics of the grandparents that you didn't see in the hybrid parent. Also, overall hybrid vigor declines with each subsequent generation, because individuals no longer carry two different copies of each gene.
You can experiment by sprouting second generation seeds, but don't be surprised if the plant yields dry and tasteless fruit! To grow the very same tomato as before, you'll have to plant seeds from the same first generation cross. Some plant breeders do continue the breeding process through many growing seasons, selecting only the best plants until their favorite hybrids consistently produce offspring true to form.