Lagrangian points are positions in an orbital configuration of two large bodies where a small object affected only by gravity can maintain a stable position relative to the two large bodies.
The Lagrange points mark positions where the combined gravitational pull of the two large masses provides precisely the centripetal force required to orbit with them.
There are five such points, labeled L1 to L5, all in the orbital plane of the two large bodies. The first three are on the line connecting the two large bodies; the last two, L4 and L5, each form an equilateral triangle with the two large bodies.
The two latter points are stable, which implies that objects can orbit around them in a rotating coordinate system tied to the two large bodies.
Several planets have satellites near their L4 and L5 points (trojans) with respect to the Sun, with Jupiter in particular having more than a million of these.
Artificial satellites have been placed at L1 and L2 with respect to the Sun and Earth, and Earth and the Moon, for various purposes, and the Lagrangian points have been proposed for a variety of future uses in space exploration.
NOTE: Above information has been taken from wikipedia and/or official websites of topics.