There are 2 kinds of points in game : Love Points and Trust Points.
Love Points shows how close the star feels to the manager as a date. The amount of this points will affect many things in game. Raise Love Points by going on a date with the star. (Check the Points at Star's Profile).
Trust Points shows how well you manage your star. To keep high Trust Points, your star should be punctual and always try meet his schedule. It'll affect the rewards for all the activities in game. You can raise Trust Points by giving bronze graded gifts to NPCs. (Check the Points at Manager's Profile > NPC's TP).