Aight, so imagine an allele is one Lego brick, and again let's just use one trait as an example. How about the smell of the buds.
Each different smell is encoded on each allele. Let's say a blue Lego smells like berries, and the yellow Lego smells like skunk, the green smells like pine. If there are only blue Legos available the plant is homozygous, if the mother gave a blue and the father gave a green, the plant is heterozygous. If the father offered a yellow and the mother had none to offer, there's another term that I can't remember at the moment.
Granted this if hella oversimplified, it's just a way of putting breeding projects down on paper and successful breeding projects are not dependant on this knowledge. With computers and gene sequencing you can start a million plants on the equator, test each and every single plant, and tell the computer what your final plant should look like. The computer will then tell you which plants to breed together to get what you're looking for.
That is the future of breeding