When you do something aimlessly, you have no plan or purpose. You might wander aimlessly through the zoo on a summer afternoon, not sure which animal you feel like looking at.
A road trip can be a long drive directly from one place to another, or it can look more like a couple of friends driving aimlessly along country highways, heading nowhere in particular. When someone is aimless, she has no real direction or specific plan — she's "without aim." The adverb aimlessly comes from this adjective, and it's equally random and unplanned.