F1 means the hybrid has resulted from the first generation of the cross between two plants. It’s an intentional cross between two known and compatible cultivars, which brings through desirable characteristics from each while creating a new variety. Every year, the original cross must be repeated. It’s done in a controlled environment, with the pollination happening by hand.
Often the fruit or vegetable grown from each of the parents may not be particularly desirable, but the produce from the hybrid child will be. And, usually the desired F1 result will only come true in the first generation of seeds produced from that cross, and not subsequent generations, making saving the seed from the F1 plant itself not worth while. (Often, the seed from F1 hybrid plants won’t even actually grow if planted.) That seed produced by the F1 plants is referred to as F2, and it’s actually no longer even considered a hybrid. Some of the undesirable characteristics from the grand-parents may re-emerge.
F1 plants are more expensive to buy than non-hybrids, so they have to have special characteristics that will attract purchasers, such as a stronger plant more resistant to certain diseases, higher yields or an earlier harvest. F1 seed produces very reliable results, so commercial producers like them, even though the seed cost up front is more. Some people feel, though, that flavour is one thing that breeders haven’t learnt to bring through yet into their hybrids.
Companies can patent the rights to a hybrid, because it’s treated as an invention. Generally, the creator of the hybrid also keeps the identity of the parent plants used as a “trade secret.”
The opposite is “open pollinated” seed.