A takeout double is a bid used in a competitive auction to show the unbid suits. For example, East's double of 1♠ is a takeout double showing support (3+ cards) in the unbid suits: hearts, diamonds, and clubs. East might have a hand like ♠82 ♥KQ5 ♦A972 ♣K863.
If your opponents have bid 2 suits, a takeout double shows 4+ cards in the 2 unbid suits. In the auction below, West double shows 4+ cards in the unbid suits, diamonds and spades. West might have a hand like ♠AJ82 ♥95 ♦AK97 ♣863.
Strength: A takeout double shows 13+ points, including support points.
Level: Takeout doubles apply at any level. If your opponents preempt 4♥, you're not likely to have a hand like ♠A2 ♥KQJ5 ♦J972 ♣863 and want to penalize 4♥. You are more likely to have a hand like ♠KQ82 ♥5 ♦A972 ♣AQ86. If you played penalty doubles at the 4-level, you wouldn't have a way to show the unbid suits. High level takeout doubles are typically converted for penalty. Your partner needs a good reason to bid. On the auction shown below, West would pass, converting the double for penalty with a hand like ♠J765 ♥83 ♦Q854 ♣K73. West would bid 4♠ with a shapely hand like ♠A9753 ♥743 ♦KQ4 ♣7. See Larry Cohen's discussion on why you should play takeout doubles thru infinity.
A 4NT overcall overcall typically shows a 2-suited hand. On the auction below, West's 4NT overcall is artificial showing 2 places to play. West might have a hand like ♠7 ♥KQ843 ♦Q4 ♣AQ952. If West had a hand like ♠7 ♥KQ843 ♦QJ4 ♣AQ92 with 3 places to play, West would double for takeout.
Doubles are also used to show a big hand. The typical range for a 1-level overcall is 8-17 points. A 1NT overcall typically shows 15-18 HCP. With more points, you begin with a double and then bid their suit (or notrump). An exception to this is an Equal Level Conversion Double. With that agreement, if advancer bids clubs, and the doubler bids diamonds, they aren't showing an 18+ point hand with long diamonds. They are showing 13+ support points with the unbid major and diamonds. A hand like ♠A975 ♥74 ♦KQ874 ♣K7 would be typical for East on the above auction playing Equal Level Conversion Doubles. For more on this topic, see Larry Cohen's article.
Takeout doubles can be used in the balancing seat. Because your opponent's failure to invite game implies your side has at least 16 points, a balancing takeout double doesn't show strength. It shows support for the unbid suits and a desire to compete. See our Balancing article for more on this topic.
Advancing a takeout double is quite different than responding to an opening bid. On the auction shown below, West doesn't have the luxury of passing with a weak hand like ♠7652 ♥843 ♦954 ♣852. West doesn't expect to beat 1♠X. Overtricks can be very expensive. West should bid 2♣, their cheapest 3-card suit. Since the partner of the takeout double may need to bid with weak hands, a minimum bid of a new suit in response to a takeout double shows 0 to 8 points, including Support Points. See our Advancing a Takeout Double article for more on this topic.