A Lagrange point is a position in space where the gravitational forces of two large bodies, such as a planet and a moon or a planet and the sun, balance out the centripetal force experienced by a smaller body. This results in a stable or semi-stable location where the smaller body can maintain a position relative to the two larger bodies, effectively "parking" in that location.
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A Lagrange point is a stationary position in the rotating frame of the circular restricted three-body problem. The two primaries' gravitational forces and the centrifugal force balance there. Their gravitational pulls alone need not cancel.
Three Collinear Lagrange points lie on the line through the primaries; two Triangular Lagrange points complete equilateral triangles with them. Stability requires the full rotating-frame equations, including the Coriolis force. The collinear equilibria are unstable, while the triangular equilibria are linearly stable for a sufficiently small secondary mass fraction. Spacecraft can use nearby trajectories with stationkeeping; an equilibrium calculation alone does not make a spacecraft remain there.[ref]
The Lagrange Points by Neil J. Cornish. pp. 1–4: rotating-frame equilibria; pp. 5–8: linear stability and its mass-ratio condition