Every time your Hero gathers a Gem, it builds up a pool of experience that you will receive once your current game ends. 

After each game, you can watch a short video to double the amount of experience your Hero will receive for this run. 

Once you fill out the XP bar, that Hero will gain a level and the next time you play with him, you'll now get higher quality gems right off the bat.  

Each Hero starts at level 0 and can go up to level 3.