They are fixed points of the circular restricted three-body problem.  The first three are unstable to radial perturbations but the final two are in islands of stability.  The SoHO spacecraft orbits one in the Earth-Sun system
They are fixed points of the circular restricted three-body problem.  The first three are unstable to radial perturbations but the final two are in islands of stability.  The SoHO spacecraft orbits one in the Earth-Sun system, and for ten points, two in the Earth-Moon system are likely sites for space colonies built at what points named for a French mathematician.
They are fixed points of the circular restricted three-body problem.  
Lagrange or Lagrangian points