The root is the part of the plant that's underground. Dig up a potato, and you will unearth its roots. Just pull them off before you cook the potato.
Root comes from the Latin word radix, which means "starting point," and you can think of the root of something as the place it starts from, whether that's the root of a tree, or the root of a problem. The root of your fear of swimming might have been a scary shark attack movie. If your ancestors come from Guatemala, you have Guatemalan roots. If you dig through a pile of junk, you're "rooting around."