Sometimes called the "remote" or abbreviated "Tx," this is what you hold in your hands to control the vehicle. It converts your physical inputs into radio transmissions that your vehicle listens for. There are two basic styles, pistol and stick. Toy RC cars & trucks frequently use the stick type, which has a speed lever on the left and a steering lever on the right. Hobby-level cars & trucks generally have pistol-grip transmitters, with the speed control lever in the position of the trigger of a gun, and steering being done via a small steering wheel on the side. With aircraft, stick transmitters are used to allow control of movement around all axes and to handle various fine trims and adjustments.
Where there is a transmitter, there must be a receiver. This small box listens to the specific frequency (channel) of the transmitter and sends out appropriate signals to the vehicle's other components to control speed & direction. In electric RCs, this component usually derives its power from the main battery. In nitros, it is powered by a small 4- to 6-cell battery pack of its own. You'll often see the word "receiver" abbreviated to "Rx."
Radio systems are usually tuned to a specific radio frequency (channel) via to a fingernail-sized metal-encased part called a crystal or frequency chip. There's one in the transmitter and one in the receiver. Even the cheapest hobby-class RCs give you easy access to swapping these out for other frequencies to avoid conflicts with other vehicles in your area. More expensive "synthesized" radio systems let you change frequencies by turning small dials on the receiver & transmitter, and the best & latest do it automatically.
A servo is essentially a motor and gearbox that rotates a shaft within a limited arc (usually around 95 degrees in either direction). In the absence of really tiny people with tiny hands to pull levers and tiny feet to push pedals, servos provide the force to steer wheels, apply throttle, or move control surfaces.