gesticulate
To move your hands a lot while talking to show meaning.
To gesticulate means to move your hands and arms energetically while talking, using gestures to help express what you're saying. When someone gesticulates, they might wave their arms, point dramatically, or draw shapes in the air to emphasize their words.
You've probably seen people gesticulate when they're excited about something. A friend describing an amazing skateboard trick might gesticulate wildly, hands swooping through the air to show how they jumped and flipped. A teacher explaining a complicated math problem might gesticulate to trace imaginary lines and angles in the air. Someone telling a funny story might gesticulate more and more as they reach the best part.
The word suggests bigger, more noticeable movements than just casual hand gestures. If you rest your hand on your chin while thinking, that's not gesticulating. But if you're passionately explaining your favorite book to a friend, talking with your hands flying around for emphasis, you're gesticulating.
Different cultures have different norms about how much people gesticulate. In some cultures, talking with animated hand movements is completely normal and expected. In others, people tend to keep their hands quieter while speaking. Neither way is right or wrong, just different styles of communication.