When playing a game of blackjack, insurance is offered to all players each time the dealer shows an upcard of Ace. When you bet insurance, usually you will place an additional bet that is equal to half of your original bet. This bet serves as "insurance" in case the dealer has blackjack. If the dealer has blackjack then you get paid double money on your insurance bet so that, even though you lose your original bet, you still don't lose any money.
If a player has blackjack then placing an insurance bet will insure that they will receive even money. Winning with blackjack ordinarily pays out 3:2, so by placing an insurance bet you can break even when the dealer has blackjack and, even though you'll lose your insurance bet if the dealer doesn't have blackjack you'll still win even money for your blackjack.
Some people swear by the insurance bet. However, many blackjack players know that taking insurance is a sucker bet and should never be taken. Statistically speaking, it has been proven that players lose money over time when they take insurance. Therefore, unless you have bet a huge amount of money and are relatively sure (based on card-counting or similar methods) that the dealer indeed has blackjack, never take insurance.