This is where all of the power starts. An RC "battery" is actually an assembly of a number of individual battery cells, usually 5 to 8 of them, connected together to form a 6V to 9.6V pack. The most common types of cells are nickel cadmium (NiCd or "nicad"), and nickel-metal hydride (NiMH). Aircraft often use much lighter-weight, but higher-powered lithium polymer (LiPo) cells.
The motor (don't call it an "engine" if it's electric) is what actually makes the vehicle go. It works by converting electricity into magnetism to create torque, or rotational force. A small, replaceable gear is attached to its output shaft to mesh with a larger ("spur") gear that connects to the rest of the drivetrain and ultimately to the wheels.
Between the motor and battery is a device for regulating how much electricity can flow through the circuit. This can be either a mechanical speed controller (MSC) or an electronic speed controller (ESC - pictured at right). A MSC uses a servo motor to physically turn a dial connected to one or more resistors. An ESC is a generally smaller, fully-contained electronic component with no moving parts.