Two pure bred, but different, parents are cross pollinated.

The Parents are carefully selected so that the Cross has some special characteristics (disease resistance, higher yield, better flavour, whatever)

The resulting offspring are First Generation from that cross - and are termed F1

Offspring of those will be F2, and will not carry the benefit of the F1 (well, some of them might, but its not worth keeping seed from F1 varieties for that reason)

Of course ... an F1 Cross that only gives Male plants isn't going to have any offspring, unless it adopts but you know what I mean