[1] It is traditionally expressed either in metres or as a pressure difference in hectopascal (hPa, equivalent to millibar).
Sometimes, the expression cloud height is used instead of cloud base, in which case the context has to clarify whether the intent is to designate the height of the base of the cloud or the size of it.
Cloud height is measured with a ceilometer, which takes laser or other light measurements of the cloud base and cloud top altitudes.
For instance, cumulonimbus clouds can develop vertically through a substantial part of the troposphere and often result in thunderstorms with lightning and heavy showers.
By contrast, very thin clouds (such as cirrus clouds) do not generate any precipitation at the surface of the Earth.