A kind of internal combustion engine.
The vast majority of modern reciprocating engines are either inline engines (or "I") or V engines. In these two engines, the cylinders are all lined up, or lined up in two rows separated by some acute angle. In a boxer engine, however, the cylinders are grouped into two rows that are horizontally separated (that is, 180-degrees between the two).
Quite a few propeller-driven airplanes have boxer engines, but in cars, they are found only in , Volkswagens, Porsches, and Subarus. For the longest time, Porsche 911s came with air-cooled, six-cylinder boxer engines. Interestingly, VW Bugs were also powered by air-cooled boxer engines, albeit four-cylinder.
I'm not sure of all the benefits of this layout, besides the physical shape of the engine itself, which would be less "tall" than comparable V or inline engines. This may help things like keeping the center of gravity low. Also, the layout helps maintain dynamic balance (thanks farqwart). A disadvantage that comes to mind is that it makes the spark plugs hard to get to.