To ingratiate is to make obvious efforts to gain someone's favor, in other words — to kiss up to someone.
Ingratiate has not strayed much from its Latin roots, in gratiam, (in plus gratia meaning "favor") which means "in favor" or "for the favor of." To ingratiate is to gain the favor of someone by doing lots of favors to the point of being a nudge. Like the teacher's pet who answers every question, stays after class to clean the chalkboard, and brings the teacher an apple every day. When you ingratiate yourself to people, you risk annoying them — like a little dog nipping at their heels.