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According to WiseGeek

Rotary mowers have a horizontally mounted fan-style blade that spins in a circular motion. The fast sweep of the fan blade over the top of the turf cuts the grass. Rotary mowers are always powered mowers, as it takes an engine to spin the blade with the veolcity required to cut grass. Because the blade spins horizontally, rotary mowers are especially suited to lawns that are largely made of weeds, dandelions and other tall sprouting grasses. Singular tall stems or blades can be missed by reel style mowers that lay them flat, only to have them spring up again.
Weeds aside, most professionals agree that between a reel and rotary lawn mower, the reel cuts lawn more evenly and much closer than a rotary. Reels can give lawn that "putting green" look. Reels also cut cleanly, allowing grass to create a natural seal that protects it against harmful pathogens. Rotary mowers are likened more to tearing grass. When grass is torn rather than cut it might develop brown tips that can take away from the overall beauty and health of the lawn.