I'm guessing you also have an antenna, and an inside cable outlet with a button you press to turn the booster on. There are antenna and cable inputs to the booster, which are also selected with the switch.
To use the cable input, you have to turn the antenna amplifier off - that switch also switches between the cable and antenna inputs, so if it's on - no cable.
I'd guess the jack in back is the cable input to the booster, and the one by the door is for an outside TV. The booster has a splitter in it which would allow a cable signal to pass through to the other outlet (although not real well).
Where does the rear Sat connector go to? Might that go to the 3rd of the 3 outlets you mention?