Have a technical question you can't find the answer to in FAQ's? Ask it here. Game problem questions that do NOT pertain to things like training advice, what would my horse do well in, how much is it worth.
Account levelling is... well, it's adding levels to your account. For lack of a better definition.
For each five levels, you can pick a bonus. Novices can only pick a max of 5, while sponsors can pick 10. The bonuses aid in certain aspects of the game. So Better Breeder would give you better foals, Cool Competitor helps with eventing, etc.
You can level by gaining experience. You can do this while doing pretty much everything. You will gain experience when training, eventing (the best results), breeding... etc.