A grandparent is your parent's parent. Your dad's mother is your grandparent, and so is your mom's father. If you're lucky enough to have living grandparents, then that's pretty grand.
Most people have a special name for each of their grandparents, whether it's "Grandma," "Grandpa Bob," or "Nana." Others never have the chance to meet their grandparents, but everyone has them. The word grandparent, first used at the start of the nineteenth century, uses grand in its sense of "a generation older than." Your grandparents are a generation older than your parents.