Acting recklessly means doing something without stopping to think about the consequences of your action. If you recklessly throw a football near your neighbor's house, you may end up paying to repair a broken window.
The adverb recklessly is nearly the same as carelessly, with one difference: doing something recklessly implies that your action is potentially dangerous in some way. Driving recklessly is always a terrible idea, as is recklessly spending every last dollar in your bank account. This risky word can be traced back to the Old English receleas, "careless, thoughtless, or heedless."