In a system of two large bodies (Sun-Earth or Earth-Moon), these are the points where a small third body will keep a fixed position relative to the other two.
Named for French astronomer Louis Lagrange (1736-1813) who first studied them and who showed there existed 5 such points. In the Sun-Earth system only two are important, both on the Earth-Sun line--the L1 point 236 Earth radii sunward of Earth, and the L2 point at a similar distance on the night side. The L1 point is a good "early warning" outpost intercepting shocks and particles emitted by the Sun and its vicinity has been occupied by several spacecraft.
Altogether five Lagrangian points exist in the Earth-Sun or Earth-Moon system.
L4 and L5, the two dynamically stable Lagrange points, under certain conditions.