A microscope beamsplitter is a device on a trinocular microscope (a microscope with a camera port) that will direct light up the trinocular tube to the camera. There are several types of microscope beamsplitters. One type will darken one eyetube completely while directing that light to the camera. Another type will send 80% of the light up to the camera and only 20% to the eyepieces. And finally, some beamsplitters will make both eyepieces go dark and allow for full light up to the camera.
To engage a microscope beamsplitter simply pull the silver knob on the side of the microscope out. When finished capturing images, push the beamsplitter back in to redirect all light to the microscope eyepieces.
The microscope shown above is the Meiji Stereo EMZ-5TR on a PBH stand.