A plane is a vehicle that flies through the air, but it is also a tool used to make something smooth and flat, a kind of tree or a level surface. As a verb, to plane something is to make it flat and smooth.
Don't confuse plane with plain, an adjective that means "simple" or a noun that means "flat land," like the plains of the American Midwest. This can be tricky because plane describes something that is flat and level, or the tool or action that makes something flat and level. If you remember that plain applies only to landforms, the difference will be plain to see — meaning obvious.