Most likely a fuse. Cigarette lighters are built with a thermal cutout for a safety backup, and they have special contacts for the lighter element. Many accessory plugs have a side contact that can allow them to touch and ground out that safety terminal which will cause the fuse to blow. That's why most cars today have separate power outlets. They are built differently than lighter outlets.

After replacing the fuse, watch how you insert the cell phone plug and always insert it the same way, then don't rotate it once it's plugged in.