When you do something heedlessly, you don't give it enough thought first. If you heedlessly ride your skateboard through a huge parade, you'll startle the marching band, and you may spook the horses too.
If you're reckless, taking unnecessary risks without considering how your action will affect you or others, that's acting heedlessly. This adverb comes from heedless, "showing a reckless lack of care," and its source, heed, "observe" or "care for." You should never dive heedlessly into a pool without first checking to see how deep it is!