It's generally best to double down when your hand total is 10 or 11, and the dealer's upcard is weak (2 through 6). Split: If you are dealt a pair, you have the option to split the pair into two separate hands and play them independently.
Double down means you double your bet and take one hit, hoping for a ten or a facecard to make 20 or 21. If you are dealt two aces, that adds up to 2 or 12. Split those aces and match the first bet on the second hand. When you split a pair you are now playing two hands with the same bet on each hand.