http://en.wikipedia.org/wiki/Noise_(electronic)
Generally there is a certain noise floor to the signal, and it varies in the different color channels, often blue is the noisiest.
So you can sort of think of it in two ways, one is the general or average noisiness of the image/system, sort of like the grain structure of a film stock, the second is how you expose an image (in each color) relative to that base noise.
If most of the noise is in the darkest areas, then the more signal (information) you give an object to place it higher than the noise floor, the cleaner it will be. So even a dark grey area could be exposed higher up from the floor and become cleaner... the only downside being clipping at the other end for your bright objects.
So generally you expose an image as best as you can to avoid either clipping in the highlights or noise at the other end, and therefore the tonal range of the subject becomes an issue... i.e. if you are shooting an insert of a dark object that has no bright highlights, you are free to expose it more and thus lift it above the noise floor.
There is no perfect solution but obviously you have more exposure freedom if the general noise level of the system is low. This is why people can rate the new M-X sensor of the Red One camera at much higher ASA levels -- it's not so much that the new sensor is faster, but that the overall signal and system is much lower in noise so there is more freedom to place information in the lower part of the signal.
Generally you expose to the right just to keep above the noise floor, I'm not sure the linear sampling for RAW recording is the real reason. In a log recording, there are more samples allotted to different parts of the exposure curve, I'm not sure in what manner, I believe it tends to be favorable towards midtones and highlights, whereas the RAW linear recording doesn't bias one way or the other, so a certain number of bits are less efficiently being for shadow information, hence why exposing more may give you better signal to noise, but at the cost of increased clipping. But I'm not completely sure on that.