How does a magnifying glass work? I know it creates a virtual image of the observed object but how is it possible that humans can see the virtual image?

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Note that the above description is true only for a magnifying (convex) lens. For concave lenses, the beams would be bent in a different way, and the virtual image will appear smaller than the real object.

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Have a look at this image of a magnifying lens on the Wikipedia page about Optics. It shows clearly how the lightbeams from the top of the image travel trough different parts of the lens. The lens then bends them (through refraction) in such a way that, to the observer, the lightbeams appear to come from a point that is further to the left and to the top. That is the virtual image. All the lens has done is to bend the lightbeams in a way that makes them appear to come from a "virtual", larger object. In the process it magnifies the object. As the lens bends the lightbeams, we cannot see the real object through the lens, only the magnified virtual image.