Jeep Liberty/Limited Slips
Limited Slip is a traction aiding differential that will supply a percentage of torque to the tire with the most traction. It works by binding the two side gears of the differential against the carrier when a set speed difference is reached between the two gears. Essentially, if one wheel starts spinning faster than the other by a substantial amount the clutches will step in and prevent any further spin. Unfortunately, the clutches in limited slips aren't especially strong and are overcome if the slip becomes too great. For this reason, many people opt for a locker instead because it provides 100% lock up.
Posi is a slang term for the limited slip differential. Named after GM' "Posi-Traction" unit, which was built by Eaton.