Any device that incorporates an evacuated chamber in which free-floating electrons are manipulated.
A vacuum tube (or valve) is a device with an evacuated chamber (usually made of glass) that has two or more electrodes, in which electrons are induced to flow among the electrodes.
There are basically two ways to induce electrons to leave an electrode: by heating it to a high temperature or by shining light on it (photoelectric effect).
A two-element tube (diode) can be used as a rectifier, since electrons will readily flow from the heated cathode to the cold anode, but not in the other direction.
Additional electrodes can be incorporated (triodes, pentodes, etc.), and these can control the flow of electrons by creating electric fields among the electrodes. These devices can be used to amplify a signal, because a small amount of voltage on the control grid can control a very large amount of current between the cathode and anode.
A stream of electrons can be formed into a beam inside the vacuum tube, and this beam can be aimed at a phosphor (cathode-ray display tube) or a metal target (X-ray tube).
As amplifying devices, vacuum tubes have largely been superceded by solid-state devices, which are generally smaller, more efficient and more reliable, except in very high-power or high-frequency applications. Vacuum tubes are still commonly used in certain niches, including microwave generation, vacuum florescent displays, and high-criticality transient-resistant circuits.