Hero levels are something you will see from the main character stat screen from the very start of the game. They will not be available to you at the very start though. Hero levels will kick in once you reach the max character level of 30. Sometimes you will see some players with a level of something like 30/50. This means they are level 30 and then have 50 hero levels.
Before you get too excited, you will not get any ability points for gaining hero levels. So make good use of the ability points you have at the start. Gaining a hero level will give you an increase to your total health rather than any ability points.
I don’t think there is an upper limit to the number of hero levels you can get. I saw a player that was level 30/200. This should give you plenty of play time if you want to increase them. Increasing the level does not appear to alter the drop rate of rare loot.