Hit dice on a monster tells you how many and what type of dice are used to determine hit points.
In AD&D they were used as the monster's level to determine attacks, hit points and monster level for calculating experience points. They also indicated how much of a threat a monster was for a typical party.
I'm glad they chose to give us the monster's hit dice since I like rolling hit points for my monsters. It adds a little variation in the creatures you encounter as you play. Some monsters in a group will be weaker or stronger than average which helps add uncertainty to encounters.