Family
A family of languages (a language family) is a group of languages that developed from a common historical ancestor.
A language isolate is a family of one, such as Basque or Sumerian.
Comments
Some linguists have tried to establish separate terms for families with greater and shallower time-depth, or of different subdivisions within a family. Here are some of them:
None of these are as universally accepted and used as the word 'family'; a branch of a family may also be called a family (such as the Germanic family within the Indo-European family).
Origin of the term
This term was apparently adopted by linguists from biology, where a group of similar plants had been called family since the mid-18th century, if not earlier. The term is deeply entrenched in linguistics since at least the mid-19th century.
See also
Other languages
German Sprachfamilie