Breeding is the method of creating new Eggs. Putting two compatible Temtem together will produce a new Egg, and from that Egg a new Temtem will be born! Breeding is the easiest way to create a Temtem with perfect stats, since they will inherit some of the stats of their parents. Breeding will also open the door to new movesets since some of the moves will be inherited, allowing a Temtem to know techniques its species might not normally learn.
Don't overbreed your Temtem!
Each Temtem will have a genetic degradation value that will lower each time a new Egg is produced, so you can only breed a specific amount of times. When the counter reaches zero, the Temtem becomes sterile. You'll still be able to battle with it, but it won't be able to reproduce further. Genetic degradation will also be inherited by the new Temtem, so you’ll need to plan beforehand how you’re going to spend the cycles.