In blackjack, doubling and splitting can be a good strategy when you have a strong hand. When you double, you are essentially putting down two cards, and if either of the two cards is a ten or a eleven, you are likely to win the hand.
If you split, you put down one card and draw two new cards. Again, if either of the new cards is a ten or a eleven, you are likely to win the hand.
When to double and split in blackjack is a personal decision. Some people feel that doubling increases the chances of hitting a ten or eleven; others feel that it increases the chances of getting hit by another card.
Ultimately, it depends on your personal strategy.