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A 3-link rear suspension is designed to keep the pinion from rotating, thus limiting axle windup and reducing tramp. The 3-link is built with four links -- it uses a Panhard Rod in addition to the three up-down locating links. However, what is called a 4-link is different: 4-link usually refers to angled links that control both up/down and side/side movement, while 3-link has parallel links for up/down movement and is why the panhard bar is needed (to control side/side movement). The 4-link is very common with coil-sprung axles and has anti-squat and anti-dive properties and is superior in most ways. The 3-link is used for drag racing to reduce axle tramp, and in 4WD vehicles on the front axle because it's easier to fit 3-link compared to 4.
Overview
4-link -- as used by many cars such as Datsun B310 Sunny and Datsun A10 Stanza and GM's A-body muscle cars.
3-link racing suspension
3-link
3-link uses Panhard Rod to control side-to-side movement of the rear axle. It doesn't do a very good job, as the rod swings causing the axle to move a little to one side on left-hand turns, and move towards the other side during right-hand turns. However for drag racing, turns are of little concern as all the racing is done in a straight line.
Panhard Rod
A much better method for a street car is the Watts Linkage which prohibits side-to-side movement. It is slightly more complex however. It was used various cars including the 1998-2011 Crown Victoria.
Watt's Linkage
3-link utilizing 2-top links (4-link with panhard rod) may be easier to package compare to a single centralized upper link
4-link
For coil-spring rear live axles, 4-link is the standard. The length differnces of the upper and lower links imparts anti-squat quality, so that on acceleration, when weight transfers to the rear of the car (thus enhancing traction), the anti-squat limits how much the back of the car hunkers down.
Anti-dive limits body movement under braking.