When you clear a blockage or obstacle, you unclog. If water's not going down the drain in your sink, you need to unclog it — or hire a plumber.
To unclog is to remove a clog, or physical obstruction. A huge part of a plumber's job is to unclog drains, removing hair or whatever else has accumulated there. Some people recommend that you unclog the pores on your face of dirt by vigorous cleaning, to avoid getting pimples. You might also notice city planners advocating for new traffic signals or roundabouts in order to unclog the streets.