The F stands for Finial, the 1 stands for first, so F1 means a first generation hybrid of 2 parent plants, they are usually selected for specific traits, which breeders hope to pass on to the F1, when they get it right they know which 2 plants to cross to get a specific F1.
they usually produce better results than the standard seed, but also cost more, plus any seed they produce, if they produce any at all will not produce new plants of the same quality

F1 is first filial [as in brother] generation. you are the F1 to your parents!
As Derek says they are know to posses specific traits, eg mildrew resistance, or better flavour, or small fruits etc. The cost is down to the breeding, research and years of trying to get the correct combination.

if you get seed from these and grow them then the new plants are F2 [grand children if you like]

The parent plants are the products of two lines that have long been inbred. The parents are often mediocre garden plants themselves, since the desired characteristics the breeder was looking for are accompanied by defective recessive genes. When the cross is made, the offspring are very consistent in their characteristics, since both halves of each parent's genes are nearly identical. They are also very vigorous, heavy bearing plants, because the defective recessive genes of one parent are cancelled out by the fully functional dominant genes from the othe--called "hybrid vigor" by plant breeders. Outside of the problems using the seeds to plant next year, most hybrids require extra fertilizer and moisture to support their unusually fast growth, and heavy bearing.

Sorry I meant to type filial, not finial, {don,t know where that came from}lol

were you thinking of onions at the time? there are onion finials on our grandfather clock :o))

Probably SBG, lol