Powerups are found in chests, in the Star Tiki, and in the free mail package you get on the main Race screen.
When you open a chest, you will get a number of Powerup cards. When you open a chest you can see a summary of how many cards are in that chest, and what the rarity means.
You may win a brand new Powerup, which unlocks that Powerup on the Powerup screen and allows you to add it to your Powerup deck.
You may also get cards for a Powerup you already own. Those extra cards are how you upgrade your Powerups and make them stronger. As you earn more cards, you fill the upgrade meter for that Powerup. Once your meter is full, you can hit the Upgrade button for that Powerup.
Upgrading your Powerups makes them stronger and more effective, and is a key strategy for winning races. It also is the best and fastest way to earn experience and level up your game.