Positions in space where the gravitational pull of the two large masses precisely equals the centripetal force required to rotate with them.

The five gravitational balance points between two orbiting masses. The first Lagrange Point (L1) is in between the two bodies. more! and more

The points in the vicinity of two massive bodies (such as the Earth and the Moon) where each others' respective gravities balance. There are five, labeled L1 through L5. The first three lie along the centerline between the centers of mass between the two masses: L1 is on the inward side of the secondary, L2 is on the outward side of the secondary, and L3 is on the outward side of the primary. L4 and L5, the so-called Trojan points, lie along the orbit of the secondary around the primary, sixty degrees ahead and behind of the secondary. L1 through L3 are points of unstable equilibrium; any disturbance will move a test particle there out of the Lagrange point. L4 and L5 are points of stable equilibrium, provided that the mass of the secondary is less than about 1/25.96 the mass of the primary. These points are stable because centrifugal pseudo-forces work against gravity to cancel it out.