A halo orbit is a type of orbit around an L1, L2, or L3 Lagrangian point. It is periodic, in that it follows same path each cycle other than the slow degradation due to the point's instability (which can be handled by stationkeeping). Such orbits can allow a line of sight around the body in the middle, such as an orbit beyond the Moon that always has a line of sight to stations on Earth. They also help allow multiple spacecraft to operate "at" (near) the same point, such as all the spacecraft at Earth-Sun L1 and L2.
Two other kinds of orbits are possible for use at the L1-L3 points: a Lissajous orbit, which is not periodic in the same sense. With each cycle, the path is different, but I believe they remain in a cylinder-like thin curved volume. Lissajous orbits are now more commonly used than halo orbits. A Lyapunov orbit is also aperiodic, but remains in a plane. I suspect halo orbits and Lyapunov orbits can be looked at as special cases of Lissajous orbits, but I haven't seen this stated.
|Lissajous orbit||aperiodic||not within a plane|
|Halo orbit||periodic||not within a plane|
|Lyapunov orbit||aperiodic||within a plane|
I also suspect some or all of these can be used with L4 and L5, which haven't been as popular for use by spacecraft, and less is written about their possible orbits.