I know you asked lino, I hope you don't mind me giving an example regardless.
A good example is breeding in auto traits.
If you cross a photoperiod plant with an auto, all the F1 will be photo plants. If you cross two F1, some (roughly 75%) will be photos, the rest autos. If you pick two of those autos, you will have only autos, which will produce only autos every generation.
From that you can derive:
AA is photo
aa is auto
AA caps because photo dominates auto, making auto recessive.
The F1, based on punnet, are all Aa (one side can contribute only A, the other only a). This is why F1 should be extremely uniform, but is not stable for breeding.
Crossing two F1, so Aa with Aa, gives based on punnet results, 25% AA, 50%Aa, and 25%aa plants.
AA is photo, aa, is auto, but Aa is also photo just like all the F1. The A (photo gene) is "complete dominant" over the a (auto gene) so a doesn't get to express itself. So, you get 75% photo, 25% auto.
Breeding a trait true, pure, means crossing homozygous with homozygous, which in this case means crossing an aa plant with another aa plant.
So when you pick two autos in the F2, you get punnet aa x aa which is all aa in every plant, which means auto is bred true.
That's an easy example because the desired trait is recessive. Recessive traits only show when they are homozygous.
Imagine however, having to breed photo "true" from that F1. The only way to do that, is to breed out the 'a' gene, which in turn is done by crossing two AA plants.
In that case you cross the F1 into F2 to recombine the Aa plants into that typical F2 ratio 1:3:1, giving you 25% AA, 50%Aa, and 25%aa plants.
From that you need to pick two AA plants, but how do you distinct AA from Aa plants? If you pick two Aa plants (photoperiod
phenotype but not homozygous genotype) you will end up with that same ratio again, again with photo and auto plants. If you pick one AA plant and one Aa plant, you get according to punnet results 50% AA, and 50% Aa. They will be all photoperiod plants, but it will not be bred true, it will not make good breeding stock for a photoperiod F1 as long as that 'a' is in there.
And that's where understanding Mendel's work comes into play, it's what allows you (through test crosses and/or observing inheritance every generation) to select that AA instead of the Aa. That the phenotype-genotype distinction thing I linked to.
If this like a lot to take in, punnet squares are easier than multiplication and division, which we all had to do a few times to before it goes automatically.
Again, there's more to it than Mendel's simple rules of inheritance and doing punnets, but it's it has been the foundation for plant breeding for about a hundred years now. It's indirectly what resulted in the green revolution.
http://en.wikipedia.org/wiki/History_of_plant_breeding