There are two types of Experience (XP) in Sins of a Dark Age: Account Experience and Hero Experience.
Account Experience[]
You can currently only gain Account Experience from participating in Quickplay matches. The current Account level cap is 30. Upon leveling up, you should receive a Promotion Chest with free loot. You do not need a key to open a Promotion Chest.
Hero Experience[]
Hero Experience is needed to gain new levels to unlock more abilities. The maximum Hero Experience level is 15. You can gain Hero Experience from killing minions, enemy heroes, and completing quests. Enemies that die near your hero also grant experience, but contributing to those enemies' deaths grants more experience than just passively standing close.
The Experience needed to reach the max Hero Level is:
1-2: 390
2-3: 550
3-4: 710
4-5: 880
5-6: 1040
6-7: 1210
7-8: 1360
8-9: 1540
9-10: 1690
10-11: 1860
11-12: 2020
12-13: 2190
13-14: 2340
14-15: 2550
Note: Although level 15 is the Experience Level cap, the Experience Level tooltip shows that the next amount should be 2640. However, experience is disabled and no longer received at level 15, and this number may just be extraneous information.