In the vicinity of two bodies in space that orbit each other lie five Lagrange points, named after Joseph-Louis Lagrange, the French / Italian mathematician (1736-1813). Lagrange made major contributions to various branches of mathematics, and discovered the Lagrange points in 1772 while working on the three body problem, first described by Sir Isaac Newton in 1687.
The diagram at the left shows the location of the five points. The Earth-Moon system has five Lagrange points, commonly labeled EML-n, and the Sun-Earth system has five points, labeled SEL-n:
L-1 is, as one might suspect, located between the two bodies, where the gravitational pull of each body equals the other. This point is unstable. That is, if a satellite deviates in any way from the point, it will fall into the gravity well of one or the other bodies. The Solar and Heliospheric Observatory (SOHO) is located at SEL-1 in a Halo Orbit.
L-3 lies beyond the larger body away from the smaller body. SEL-3 is on the other side of the Sun from the Earth.
L-4 lies at the corner of an equilateral triangle whose base is between the two bodies, ahead of the direction of the orbit of the smaller body. The Trojan asteroids occupy SJL-4 and SJL-5 of the Sun-Jupiter system. Both L-4 and L-5 are stable, as shown by the gravity contours in the diagram.
L-5 lies at the corner of an equilateral triangle whose base is between the two bodies, behind the direction of the orbit of the smaller body. EML-4 and EML-5 were popularized by G. K. Oneill as places to build human space colonies. This was the impetus for the founding of the L5 Society.
Wikipedia has an excellent article on Lagrange points in space.