If you've ever done something without stopping to consider the consequences, you did that thing unthinkingly. If you unthinkingly make a joke about short people, it might offend your vertically challenged friend.
Some actions require extremely careful thought. You wouldn't want to unthinkingly get behind the controls of an airplane or unthinkingly follow your best friend's instruction to jump off the roof into a pile of leaves. There are less obvious things you might do unthinkingly that also have big consequences, like unthinkingly making assumptions about other people, or unthinkingly believing the gossip you hear. In all of these cases, you're acting without thinking.