Hi Svetlana, a "witty repartee" is an exchange, a quick, stylish conversation or a clever comeback. Maybe you've seen the 2 comedians Abbott and Costello ("Who's on First")?
A witty repartee is usually used in a "double act" where there are 2 players who have a routine with fast replies and comebacks. Often there is a straight man, who sets the joke up and then a gag man or funnyman who delivers the comebacks and retorts. Do a YouTube search on "Who's on First" if you've never seen Abbott and Costello.
Witty repartee can also just mean a clever conversation that's not part of an act, of course.
Some people can answer you with a witty repartee, pun or turn a phrase very quickly. A witty repartee is also called "a snappy comeback"