Lagrange points: The points in the vicinity of two massive bodies (like the Earth and Moon) with each others' relevant gravities balance. There are five, labeled L1 via L5. L1, L2, and L3 lie all along the centerline among the centers of mass between the two masses; L1 is on the inner side of the secondary, L2 is on the external side of the secondary; and L3 is on the external side of the primary. L4 and L5, the so-called Trojan points, lie all along the orbit of the secondary about the primary, 60 degrees ahead and at the back of the secondary.
L1 via L3 are points of unstable equilibrium; any trouble will move a test particle there out of the Lagrange point. L4 and L5 are the points of stable equilibrium, given that the mass of the secondary is less than around 1/24.96 the mass of the primary. Such points are stable as centrifugal pseudo forces work against the gravity to cancel it out.