Hi Platinum and welcome to WAB!!
I haven't got a 350D, but the basics are still the same ....
Exposure compensation allows you to adjust the exposure measured by its light meter. This means that you can tell the camera to allow more light in (positive exposure compensation) or to allow less light in (negative exposure compensation). Depending on how your digital camera deals with exposure compensation (and the shooting mode used), it may adjust the aperture whilst maintaining the shutter speed, it may adjust the shutter speed while keeping the aperture constant, or it may adjust both the aperture and shutter speed.
Why would you want to do this?
Because there are certain situations where the light meter of your digital camera can be fooled.
As an example, say you are taking a scene where there is an abundance of light around your main subject (for example, at the beach on a sunny day, or surrounded by snow). In this case, using Weighted-Average metering, your camera might be 'deceived' by the abundance of light and expose for it by closing down the aperture and/or using a faster shutter speed, with the result that the main subject is under-exposed. By dialing in a positive exposure compensation (say +1EV), you are making sure that your main subject is correctly exposed, although the surroundings would be overexposed.
Another example would be the case where the surrounding might be too dark, and the camera exposes for the lack of light by either opening up the aperture and/or using a slower shutter speed, then the main subject is over-exposed. By dialing in a negative exposure compensation (say -1EV), you would in fact be under-exposing the surroundings, but properly exposing the main subject.
Many photographers will bracket their exposure when taking an important shot by taking one shot using the camera's measured exposure, a second one at positive exposure compensation, and a third one at negative exposure compensation.
Many digital cameras now include Automatic Exposure Bracketing (AEB) where the camera will take three shots with one press of the shutter release button: one at the camera measured exposure, a second at a negative exposure compensation (usually -1/3 EV, though some cameras allow you to specify the amount), and a third at a positive exposure compensation (usually +1/3 EV).
As with a lot of these things, I have found that trial and error is the best way of learning these things – and of course, that's the beauty of digital – you can shoot away to your heart's content without wasting film!
Best of luck!!
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