The 'doosra', an Urdu word meaning 'the other one', is a delivery in cricket made famous by Sri Lankan off-spinner, Muttiah Muralitharan. Murali is a finger spinner - in that he uses his fingers rather than his wrist to make the ball rotate, but with the doosra he also rolls his wrist over the ball, altering the direction of spin, and thus the behaviour of the ball.
Essentially the doosra ball is the moral equivalent of the better known googly ball, in that it spins in the opposite direction to the bowlers stock delivery. In the case of the googly the ball moves across the batsman from off stump to leg stump, in the opposite direction to a normal leg spinners delivery. The doosra works in the same manner, in that an off-spinners stock delivery usually moves from off to leg, whereas the new ball moves from leg to off.
There has been a great deal of controversy over the new delivery, mostly accusations that Murali is a 'chucker' implying that due to the extra wrist movement, he was throwing the ball rather than bowling it, which is illegal in the game of cricket. There have been several biomechanical studies of Murali's bowling action before due to complaints made by match officials, as his arm is bent during the delivery. His claims, which have been largely backed up by medical scans, that he has a congenital condition that means he cannot fully straighten his elbow. The relevant laws permit this as long as the arm stays in the same position throughout the delivery and the elbow isn't flexed.