Thoroughly means exhaustively and completely. No matter how thoroughly you clean every carpet, shelf, and windowpane in a house, there is always more dust to be found.
Thorough comes from the word through, and originally meant passing completely through something. We use thorough and thoroughly now to show that we have really been as meticulous as possible in a given task. If a detective interviews everyone present at the scene of the crime, collects all the biological evidence, and takes pictures from every angle, then we can say she investigated the crime thoroughly