A cell phone booster pulls in a weak signal from the outside, boosts it and then rebroadcasts it within the house, building or vehicle. A typical signal booster is based on a three-part system.
It consists of an outside antenna that captures the weak cell signal, an amplifier that boosts the signal thus received, and an inside antenna that rebroadcasts the much enhanced signal within the room, house, building or vehicle.
An outside antenna is mounted in a location outside the house or building which currently gets a signal, usually on the roof. This signal is then passed from outside antenna to a signal amplifier within the building. An amplifier enhances the signal by up to 32X times and then sends it to the inside antenna. An inside antenna rebroadcasts the signal to the area where it is needed the most.
That is how you get a much improved signal from the cellular tower. The same process works in the reverse. The signal from your phone is picked up by inside antenna, enhanced by amplifier and sent out to the outside antenna, which rebroadcasts it so that a much stronger signal is received by the cellular tower. This establishes a strong two-way communication between your phone and the cellular tower.