A missile is, broadly, a projectile, that is, something thrown or otherwise propelled.
Missiles can range from a rock thrown from a slingshot through a crossbow bolt to a Minuteman III intercontinental ballistic missile with multiple nuclear warheads. The largest missiles currently deployed represent the most destructive weapons ever made.
Missiles are often used in warfare as a means of delivering destructive force upon a target. Sometimes missiles are used to deliver other payloads. For example in the Kuwait war cruise missiles were used to deliver reels of carbon filament to electricity stations and switches, effectively disabling them by forming short circuits.
Missiles with no ability to maneuver are called ballistic missiles (because their motion is governed by the laws of ballistics). Whilst quite a wide term, unqualified use of the term ballistic missile is likely to mean an initially rocket powered medium- to long-range missile; classicly the ICBM.
Missiles that have the ability to maneuver can be guided, known as guided missiles. There are 3 key components:
A tracking system locates the missile's target. This can be either a human gunner aiming a sight on the target (remotely from the missile) or an automatic tracker. Automatic trackers use radiation emanating from the target. Passive automatic trackers use the target's inherent radiation, usually heat or light, but missiles designed to attack Command and Control posts may use radio waves. Active automatic trackers rely on the target being illuminated by radiation. The target can be "painted" with light (or infra-red) or radio waves which can be detected by the missile. The radiation for the painting can originate in the missile or from a remote station (for example, a hilltop gunner can illuminate a target with a laser device and this can be used to direct an air launched guided missile).
A guidance system takes data from the missile's tracking system and flight system and computes a flight path for the missile designed to intercept the target. It produces commands for the flight system.
The flight system causes the missile to maneuver. There are two main systems: vectored thrust (for missiles that are powered throughout the guidance phase of their flight) and aerodynamic maneuver (wings, fins, etc).
There is some blurring between guided missiles and guided bomb. A guided bomb is unpowered and dropped from an aircraft but apart from that shares many characteristics with the guided missile.