Sprites upgrade your characters by giving them new or changed behavior. You can change your sprites by tapping on one of the circles above your characters heads.
You can get new sprites by opening Sprite Box, or randomly from other gift boxes.
Sprites will have text above them that say forever or one use. Forever sprites will give their bonus as long as they are equipped. One use sprites will only give you their bonus for the next run, then disappear.
Permanent sprites can be upgraded to increase the power of their bonus. Tap on a sprite to see what you need to upgrade them at the bottom of the screen.
Sprites can also be sold for rings. Tap on any sprite and you can see a sell button in the lower left.