If this is a Whirpool manufactured washer (includes Kenmore, Estate, Kelvinator, Kitcheaid, Frigidaire, Roper and others), the agitator has a split design. The lower portion is the agitator, while the upper portion is called the auger. Under the auger is a cam drive. The cam acts as a clutching mechanism that drives the auger when the agitator moves. The cam has small plastic teeth called "dogs" that commonly wear out causing the auger to slip. The following link explains how to replace them:
The part number is included in the link and can be purchased at appliancepartspros.com for about $5. For a little more you purchase the entire cam replacement kit which includes the cam, bearing, any seals, and the dogs.
If this is not a Whirlpool manufactured washer, or simply don't know, please post back with your complete model number (located under the washer lid along the tub rim on most washers).
If you have questions, or require additional assistance, please let me know. I hope this helps you.