There are two basic camshaft designs: flat tappet (lifter) or roller tappet. As can be imagined, the flat tappet has a flat base which follows the camshaft lobe, while the roller lifter has a wheel at the base.
The purpose of a lifter is to translate the rotating motion of the camshaft into the reciprocating motion --- up and down --- of the valvetrain. The lifter imparts its motion to the pushrod which, in turn, transfers that action to the rest of the valve components (rocker arm and valves).
The design of flat tappets is not actually perfectly flat. Instead, they have a very slight radius on the bottom that --- when operating --- causes them to rotate within the lifter bore. This keeps the base of the lifter and the lobe of the cam lubricated. Flat-tappet cams have been replaced by more efficient roller-tappet cams in production engines, beginning in the mid-1980s.
While no longer common in modern production engines, the flat-tappet cams are still popular in aftermarket engine builds due to their simplicity and low expense. However, changing oil compositions --- based on stricter emission standards --- has resulted in an increase in flat-tappet cam and lifter failures. Used with proper oil additives, they can still offer meaningful performance and reliability.