A type of bicycle on which you ride in a low seated position. Recumbent enthusiasts also call them "bents". Rather than leaning forward, like on a traditional diamond frame bike, you sit with your back against a raised seat and cycle with your legs out in front. This makes riding more comfortable because a lot of stress is relieved from your neck, shoulders, back and buttocks. Recumbents are not as new an invention as you would think; early models like the Challand's Normal Bicyclette have been around since late 1800s.
There are three main styles of recumbents: Long wheelbase (LWB), short wheelbase (SWB) and compact long wheelbase (CLWB) bikes. Long wheelbase bikes are comfortable, fast and stable but may be tricky to handle at low speeds due to their length. Short wheelbase bikes have the front wheel situated under or a bit ahead of the rider's knees and the crankset mounted on a boom in the front of the bike. Smaller size makes them easier to maneuver and transport than LWBs. Compact long wheelbase bike is basically a cross between the long and short models and is probably the easiest recumbent to learn to ride on.
Examples of recumbent brands:
LWB: Linear, Infinity
SWB: Counterpoint Presto
CLWB: BikeE, Linear
Sources:
FAQ for Recumbent Bikes - http://www.ihpva.org/FAQ/
The North Texas Recumbent Bike Enthusiasts - http://www.rbent.org/