1640s, "point of convergence," from Latin focus "hearth, fireplace" (also, figuratively, "home, family"), which is of unknown origin. Used in post-classical times for "fire" itself; taken by Kepler (1604) in a mathematical sense for "point of convergence," perhaps on analogy of the burning point of a lens (the purely optical sense of the word may have existed before Kepler, but it is not recorded). Introduced into English 1650s by Hobbes. Sense transfer to "center of activity or energy" is first recorded 1796.
1775 in optics, "bring into focus" (transitive); 1807 in the figurative sense, from focus (n.). Intransitive use by 1864, originally in photography. Related: Focused; focusing; less commonly focussed; focussing.