If something happens painlessly, it doesn't hurt at all. When you get your ears pierced, go to an expert — they'll do it painlessly.
Things that seem scary (and potentially painful), like going to the dentist or getting blood drawn at the doctor's office, can almost always be done painlessly. In a more figurative sense, things that aren't stressful or difficult also happen painlessly. If you worried about your big math test for a week, you probably felt relieved when you zipped through it painlessly!