The question of whether or not a toilet seat can be repaired is a little silly; of course you can. The real question is why would you? Generally, the less time working on toilet seats, the better.
There aren’t many things that can go wrong with a toilet seat. If there is a problem, it is just that the seat is loose and needs to be tightened. Wear rubber gloves when touching the nether regions of the seat and underneath the bowl. Check that the hinges are tight at both the lid and the seat. If you can move the seat side-to-side, then the nuts under the bowl are loose (this is a good time to put on the aforementioned gloves).
At the rear of each hinge is a cap you can pop up to expose the head of a plastic bolt. You can tighten this bolt while holding the nut underneath still (some nuts have a little arm that keeps them from turning). Once you have the seat snug, just pop the caps back down to cover the heads.
If the seat is damaged, like a crack or if the finish is no longer smooth, just replace it. It just isn’t worth the work, when you can replace it in 5 minutes.