Uh... What's an ultimate?

hint: people think it's a pirate's favorite letter

The ultimate is the last ability each champion has. If you haven't rebound your keys at all, it's the one associated with the R key on the keyboard. It's generally the strongest ability a champion has, and is only available to level once the champ hits level 6 (with some exceptions such as Karma and Nidalee), which is an important power spike in the game.

YoUr UlTiMaTe Is YoUr R kEy

Your Ultimate, commonly referred to as your "Ult", is the fourth and generally most powerful ability of your champion. By default, it's bound to your 'R' key.

You can only put three skill points into your Ult, unlike your other abilities wherein you can put five skill points each. You generally don't get to put your first skill point into your Ult until you reach level 6 in-game. You can put a second skill point into your Ult at level 11, and a third skill point at level 16.

Most Ults greatly increase your champion's power as soon as you put a point in it. That is why it is generally a race between you and your enemy to see who gets level 6 first. If you get level 6 first, you get a window to use your Ult and kill your enemy, who is still level 5 and doesn't have his own Ult yet.