The phrase "hold on" means "wait". For example:

Hold on — you might be able to recover it.

Hold on. Just hear me out first.

You tell someone to "hold on" when you want them to wait for a short time. You use "hold on" instead of "wait" when the reason for the listener to wait is not that important. In an emergency situation, you would clearly yell "Wait!". But in normal conversation, "hold on" usually fits better.