Traditionally, a plant breeder created better crop varieties by crossing (with controlled pollination) two parents who each had good traits, and then selecting the individual offspring with the best combination of those traits.
Although this sounds straightforward, all organisms are highly affected both by their inherited genetic traits (i.e. "nature") and their environment (i.e. "nurture"). When a plant breeder walks into her field, she has no way of knowing if the "best" offspring (e.g. the ones with the highest yield, pest resistance or cold tolerance) really have the best combination of genetic traits (alleles), or whether they have inferior combinations of alleles but were lucky enough to be planted in a particularly nourishing part of the field (even the most flat and boring field has huge variations in water and nutrient availability).
When a breeder knows some of the gene alleles she's trying to keep in the offspring, marker-assisted selection (MAS) allows her to directly test which individuals have the alleles she wants. MAS is basically a genetic "fingerprint" test of each individual offspring. It's one of those (very common) situations where biotechnology is used to make non-GM crops (as the genomes are only manipulated by choosing which pairs of plants to cross). Potentially, you could test the genetic properties of the offspring before you even plant them!
A few months ago, I saw a presentation on how Pioneer Hi-Bred sorts through tons of corn, individually tests each kernel for its genetic properties and then plants only the individuals they want. A team of scientists and engineers invented this system, Laser-Assisted Seed Selection, which is one of the most brilliant and elegant inventions I've ever seen.
Each cob is mounted on a rotating peg and sprayed with magnetic paint.
The kernels are knocked off the cob and all debris falls away except for the kernels themselves, which are caught by a magnetic holder (notice only the "outside" edge of the kernels have paint on them).
A laser is used to slice off a thin piece of each kernel.
The big piece contains the embryo and most of the endosperm. It is still viable to plant and is automatically sealed in barcoded-plates and stored until it's needed. The thin sliced piece is dropped into a corresponding barcoded-plate and sent to the molecular biologists to test for genetic traits. The breeders can then order whichever genotypes she wants to plant!