Homogenisation
This process makes the mixture uniform and creamy. To maintain the mixture stable, it should contain emulsifiers, able to bound not mixable molecules, like fats and water.
As reminder: yolks and milk already contain natural emulsifiers.

Maturation
The main function of this process (lasting 6/8 hours) is to let the proteins and stabilisers absorb the water (free in the pasteurised mixture).