Gravitationally-stable points in the orbital system of two bodies. A smaller object placed at one of the Lagrange points will remain in stable orbit indefinitely (disregarding perturbations from third, fourth, fifth, nth bodies).
In any two-body system like Terra/Luna or Sol/Jupiter, there are five Lagrange points (named after their discoverer). This diagram illustrates the locations of the five points:
Of these points, L1, L2, and L3 are point-stable -- that is, a body that wanders away from the exact Lagrange point will be further deflected, eventually drifting away entirely. L4 and L5 are meta-stable, meaning that a body which moves away from the exact point will tend to drift back. In practice, small bodies take up kidney-shaped orbits around the L4 and L5 points.
In any two-body system, the Lagrange points tend to collect dust and small meteoroids. In the Sol/Jupiter system, substantial asteroids have collected at L4 and L5 -- these asteroids, given the names of Trojan heroes from the Iliad, give the L4 and L5 points their alternate name of "Trojan Points."
A system's Trojan Points are generally ideal for locating space
settlements.