Wrist-spin bowling is the correct term for what many people refer to as Leg-Spin bowling.
Leg-spin bowling by virtue of its name suggests that it's restricted to one kind of bowling action... the Leg-Break but as you learn about this particular form of bowling, you come to realize it's the collective term for one bowling specialty within cricket.
Bowling within cricket has a number of different methods for dismissing the batsman, some through brute strength, speed and the threat of injury (fast bowling), others through what's describe as flight and guile, using variations in spin, speed, loop, dip and a couple of magical things called 'Drift' and 'Swing', where the ball changes its trajectory whilst in flight.
The form of bowling with the greater amount of variations with these attributes is Wrist-Spinning and it therefore is seen to be one of the more threatening methods of attack when utilized properly - for instance by the greatest exponent of the art - Shane Warne.
Unfortunately when not used properly against good batsman you have a tendency to get hit to all regions of the ground for 4's and 6's. Kids have a tendency to pick it up relatively easy when they're young and have high degrees of success with bowling it taking loads of wickets . As kids grow older and sort themselves out into specialties, the need to develop your bowling and take it as seriously (as the batsman do), seems to dwindle and that coupled with being hit all over the park tends to put kids off of bowling wrist-spin. This situation is further exacerbated by the lack of knowledge of wrist-spin at club level and a lack of coaches able to support wrist-spinners. But, if you stick at it and practice and can take the rough times with the good times, over a number of years you'll develop the skills and tactics to be a very effective member of your teams bowling attack.
The term wrist-spin comes about because the variations in the way that the ball spins through the air as a result of the wrist position at the point of release. Wrist spinners with the full range of deliveries have the ability to bowl the ball spinning both left and right, backwards and forwards and variations in between. The most common method performed by right-handed bowlers is known as a 'Leg-Break' - this is a delivery that is released with the ball spinning clockwise as the batsman sees it coming down towards him. Amongst Wrist-spinners, this is known as your 'Stock-ball', the ball you bowl the most that generally gets you the majority of your wickets.
The way the spin is produced is through a combination of flicking the ball from the hand through use of the fingers and the wrist at a very basic level. Delve deeper and the you come to learn that the whole body is involved in order that you put the maximum rev's on the ball, but we'll come to that later.
Wrist Spinners that bowl left-handed have historically been known as 'China-man bowlers' but in today's increasing en-lightened times this term is being discouraged because of its history and derogatory nature and should be simply termed 'Left arm wrist-spinners'.
Some of best known exponents of the art...
My mate Stuart Macgill (Australia)
Clarrie Grimmett Australia
Richie Benaud Australia
Mushtaq Ahmed - Pakistan
Shahid Afridi - Pakistan
Anil Kumble - India
Bhagwat Chandrasekhar - India
Abdul Qadir - Pakistan