Most ordinary magnifying devices use a lens. Lenses are usually made out of glass or plastic, which are transparent, but those materials have an important effect on the light that passes through them.

Have you ever heard that water "bends" light? If you don't know what I'm talking about, take a clear glass, fill it with water and put a pencil in it and notice how the pencil looks like it's split in two. This is called "refraction." Light behaves differently in the water than it does in the air. The same effect is found in materials like glass and plastic.

A lens has a dish-shape to it, which causes the light rays entering it to change direction. The "focal point" is the point in space where those rays come together and the image you are looking at comes into focus, and looks bigger (or smaller if you flip the lens around).

Magnifiers bend the rays of light coming from something to make the object appear closer than it is (It is closer, not bigger). I'd need to draw a picture to show it more clearly, but the rays go from coming out of a point to being parallel.

As you know, magnifiers cannot actually make things change size or make them less fuzzy--they just change how things appear to you. They do this by rearranging rays of light. You see things because your eyes receive many rays of light, and then your brain puts together the picture from those rays. When rays of light hit a magnifier, the magnifier changes all of their directions. If they do this in a clever way, they can make things seem bigger or clearer.