Miki's party is the the group composed by Miki Kurusu's personal friends who travel at her side in an effort to retain her humanity. The group doesn't want her to become the Demon King and travels all over the land looking for a way to turn her into a human again by any means necessary.
They are constantly running away from the factions of the Monster Realm.
The Kayblis Faction wish to kill Miki to turn Kayblis into the Demon King, which makes them their most dreaded enemies and they are constantly escaping from their assaults, since they stand no chance of defeating such a powerful force of Dark Lords on their own mainly due to the large difference in numbers.
The Hornet Faction wish to turn Miki into the next Demon King and make her the new head of the Monster Realm, which is not what Miki wants. They are considered allies, and they've even befriended some of their members, since they are constantly fighting the Kayblis Faction and adding them. However, their goal is still different, and are constantly trying to convince Miki to become the Demon King, since they don't want to force her, which makes them to run away from them as well.