Champion levels are the levels your hero can obtain after reaching level 70 (since update 1.2.57 you gain them after each level increase even under level 70). You can enter these levels by each class from the same level and they stack up for each character that has reached these, so if you will be Farming these only from one class, they will be also added to your other heroes. These levels are harder to obtain when reaching levels of 200 and the Experience needed to get to next level is also increased.
Best farming levels for this are: Canyon of Whispers, The Levanian Jungle. You can also try Trials but the rewards from there only grow when reaching the high ones of 500 or more.