To march is to walk with deliberate, short steps that fall in a regular rhythm. You can take your time walking into school in the morning, or you can march right up the steps and through the door.
People can march just about anywhere they walk, although the verb brings to mind military processions of soldiers who march in unison. Marching bands are another example of people who march together this way. You can also use the word when you're talking about a group of demonstrators who decide to march in protest or support of a particular cause. March comes from the Middle French word marcher, which originally meant "to trample," and later came to mean "to walk."