What is a hit die?

Hit dice (singular hit die), abbreviated HD, are a rule in Dungeons & Dragons originally referring to the number of dice rolled to calculate how many hit points a character or monster begins play with. This determines how difficult they are to kill.

What does it mean to spend a hit die?

Hit dice are spent to regain hit points during a short rest. You spend a hit die by rolling it and regaining hit points equal to the result + your Constitution modifier. Spent hit dice are regained by taking long rests.