Breeder level is the indication of how experienced you are with training your monsters. There are 25 max levels, and with each new level you gain (including the first) you get one skill point. You also get skill points for every god you kill, equally up to 35 maximum skill points you can add to your skill tree. The skill tree is where you can customize your breeder and their attributes in training the monsters. You're going to need to put so many points in a tier of a tree before going to the second tier.

Tier 2 is 3 skill points.
Tier 3 is 7 skill points.
Tier 4 is 12 skill points.

License

Doesn't come into play until around Insula, but for each rank you have, you'll make 200 bux more for your nightly income.