A Hit Die
represents a type of die (d6, d8, d10, etc.) that a creature has its hit points
based on. I.e. if a creature has 6d8 hit dice you would roll 6 d8's and add the total (plus constitution
modifier) to get the total hit points.
Adventurers (and some creatures) can "spend" a hit die during a short rest to regain a number of hit points back (up to it's hit point maximum). Half of these spent hit dice are restored at the end of a long rest.