Anthony,
The tester has a male plug which plugs into the female CRT socket on the TV chassis. How the tester actually works, however, is a mystery to me, as it connects to the TV's signal circuits, not to the CRT itself. I've never seen anything like that in over 30 years of working with TVs and other types of electronic equipment, so can't shed any light on it.
The unit was manufactured by Vidaire, which made CRT brighteners in the '50s and '60s.
BTW, I just read the description of this beast on ebay. From what I can see, the tester is supposed to indicate the presence, or lack thereof, of video signal, 2nd anode voltage, and other voltages required for proper CRT operation, as kc8adu explained in his post. However, the unit can only give a go/no-go indication (is there voltage or isn't there?) because of the eye tube. If the tester had an actual meter it could give a technician an idea of how much voltage there is at any given point in the CRT circuits. This type of tester works on the same principle as the old pocket-size TV tube testers, which only showed if the filaments were intact or not. These testers were used mainly to find open tube filaments in series-string TVs and radios; without it, it would be very difficult to find the break in the filament string.