Both types of meter assume you want mid-toned objects in the scene to come out mid-toned in your picture. An incident light reading will ignore broad areas of bright or dark areas in the scene because it's pointed at the camera, measuring the light falling on the scene, rather than pointed at the scene and measuring light reflected from the elements in the scene. A picture taken of someone with dark green foliage behind them may well come out over-exposed with a reflected light meter because the meter is trying to make the expanse of foliage look mid-toned; decreasing exposure by one stop from the metered valued would probably be a better exposure. Similarly, a light stone wall might cause an underexposure as the reflected light meter tries to make the light stone into a mid-toned value. An incident light reading isn't affected by these things, so dark objects come out dark and light objects come out light.
A reflected light meter can work just as well provided you know what tonal value you want the object you're metering to be. I've never cared much for using an incident light meter, preferring to use a reflected-light spot meter. I just point it at something of known tonal value, and adjust the exposure accordingly. For example, if I meter off of green grass, I probably don't need to adjust anything since grass is usually mid-toned; if I meter off of typical light caucasion skin, I might increase exposure a stop so it looks light rather than mid-toned; if I meter off of dark foliage, I decrease exposure by a stop so it looks dark rather than mid-toned.
A short explanation with sample pics can be found here: