XP (i.e. experience points) is earned after every match you play. Players gain 30 XP each time they complete a match, and a victory gives a player an additional +20 XP. If a player concedes before turn 5, they will forfeit all XP.
As you accumulate XP, you will level up and unlock Base cards as well as the different Heroes in the game. This will allow you to build your own decks and participate in Constructed mode. You need 200 XP points in order to level up.
While XP is always awarded in Ranked and Conquest modes with each match, it's only awarded in Tutorial, Practice, and Private mode up to level 15.
You also get a Rank Up Bonus of 100 XP each time you progress from one rank to the next (i.e, from Trainee to Expert).
Completing quests also rewards you XP, among other rewards.