The Lagrange points are where the gravitational potential gradient is zero in an orbital system with two massive bodies. In English, those are points in space where the gravity of the two objects (e.g., the sun and the earth, or the earth and the moon) cancel and you can stay there more or less indefinitely.
There are 5 such points, numbered L1 through L5. L1 is along the line between the two bodies where their gravitational attractions match. The earth-sun L1 point, about 1.5 million km toward the sun from earth, is now well used; the most recent addition to the fleet there is DSCOVR, the spacecraft that returned that great sequence of the moon moving past the earth last summer. It joins ACE, SOHO and a bunch of others.
But none of the spacecraft are actually at the L1 point, because that would put them right in front of the sun as seen from earth. The sun generates radio noise, and this would interfere with reception of the satellite's signal. So they are slowly moved around the actual L1 point so that, from earth, they appear to slowly circle the sun, far enough from it that the dish antennas on earth can exclude the sun. (I think it's once per year, but I'm not sure). It does take fuel to do this, but with careful planning you can keep station for years. That's a halo orbit.
The L2 point is on the same line but not between them; it's closer to the smaller body. Similarly, L3 is on that line but closer to the larger body. (There was once a whole genre of science fiction about a "parallel earth" situated at the Sun-Earth L3 point, placing it permanently on the other side of the sun where we cannot see it. Unfortunately, our fantasies were dashed when our spacecraft saw nothing there, just as they show a lifeless, desolate desert on Mars, and an uninhabitable hell on Venus...)
L4 and L5 are in the orbit of the smaller body, 60 degrees behind and ahead of it (or maybe it's ahead and behind, I can never remember). These are the only two Lagrange points that are dynamically stable, i.e., you could put a rock there and it would stay indefinitely. The other three are metastable, kind of like balancing on a fence; it takes active control to stay there, but as long as you keep fairly close it doesn't take much energy.