It's used for mixing solids into liquids, or liquids into liquids.
It's magnetic because the mixing is accomplished by placing the container to be mixed on top of a plate that covers a rotating magnet. A small magnetic mixing bar is then dropped into the container. When the mixer is activated the bar is twirled by the rotating magnet below the plate, thus mixing the container's contents.
Fancier mixers also include a heating element below the plate so one can simultaneously heat and mix solutions. Many dry chemicals dissolve quicker and easier in warmer water.