When you buy a player, he's got a salary, say $10k.
When you train players, their salary can go up. Maybe you train a PG in passing and his salary goes from $10k to $15k.
You created $5 of salary on your player through training. That $5k is your "training exemption".
If your team is running at a loss (expenses greater than income), the amount you're losing is compared with your training exemption. If you're losing more money than your training exemption, you pay an extra penalty fee (+50% of the overage I think?).
This 'feature' was added a number of seasons back when it was in style to stock up on cash reserves and buy ridiculous $400k salary players for a short run. Made the extra salary hurt even more, unless you "earned" the right by training it yourself.