When you cook something in oil, the oil or grease sometimes pops out of the pan and falls somewhere in your kitchen. You can describe this by saying that the oil "spatters" on your stove, your counter, your floor, etc.
"Grease" is another word for "oil". It sounds dirtier, though.
Other things that can "spatter" are:
- blood (when someone is shot, for example)
- rain (when it's being described in a novel or short story)
- pee (when a man uses the toilet)