Vacuum tubes (valves in the UK) were the technology used in the first generation of electronic devices, through the first half of the 20th century.
(The name is slightly inexact, as some relatively common tubes, e.g. thyratrons, contained various gasses at low pressure, and use electrical discharges in the gas to operate.)
Starting in the 1950s, tubes were mostly replaced with semiconductor transistors, which were smaller, wasted less power (and thus generated less heat), were more robust, and eventually more reliable, etc. Vacuum tubes remain in use for a few specialized applications, however.
Classical vacuum tubes all contain one element, the cathode, which emits electrons when heated. (In early tubes, the heating element was used directly as the cathode; later tubes tended to make it separate, allowing a different electrical source to be used to drive the heater.) Another electrically separate element inside the tube is the anode.
When such a tube is placed in a circuit, current can flow from the cathode to the anode (since the former is emitting electrons), but not in the other direction. Such a tube therefore functions as a diode.
More importantly, if a third electrically separate element, in the form of a screen, is interposed between the anode and cathode, creating what was known as a triode, changing the voltage applied to that screen could control the current flow from the cathode to the anode.
This means the device is an amplifier, with the voltage applied to the screen controlling the current flow through the device. Appropriate circuitry allows the voltage applied to the screen to control the voltage seen at the anode.
Other tube types
Tubes with two screens (tetrodes) and three screens (pentodes) were also developed, along with many other more-specialized kinds of tubes.