Grease is the thick oil you use to make a machine work more smoothly. It's also the shiny, slick substance produced by cooking something in fat, like the grease on that fried chicken you made.
As a verb, grease means to make something slick and oily so it can move more easily: "You should grease the hinges to stop the door from creaking." As a noun grease is the kind of oil or fat that's solid at room temperature, whether it's the grease you use to repair a car engine or the grease you use to deep fry onion rings. Colloquially, when you grease someone's palm, you offer them money as a bribe.