Keeping drains clear of hair, soap and shampoo residue, and other debris is one of the best ways to help keep pop-up stoppers in good working order. If the stopper or mechanism is damaged, you can buy a replacement stopper and parts at Amazon. For more, see How to Repair a Bathtub Pop-Up Stopper.
A trip lever drain that operates a pop-up stopper is a slightly different mechanism in which, rather than a lift-bucket plunger that seals a drain opening at the bottom of the overflow tube, there is a spring at the end of the trip lever connecting rod.