The simple explanation is it's a canister that holds media that water gets pumped through. Examples of media are carbon,GFO,Purigen, etc. It's essentially a fancy term for what we called a carbon canister back when I started.
Pretty simple really. A media reactor is a container that water is pumped through. The water usually enters via a pump through the middle of the unit and is directed through a pipe to the bottom of the unit. The water then travels through a media of your choice and back out through a pipe to the tank. Some medias need to be tumbled like bio pellets so more room and flow are needed other you want slow but consistent flow like gfo.