A light microscope uses a light source but a electron microscope has beams of electrons focused by magnetic lenses.
The major difference in practice is resolution: the amount of detail that can be discerned in the image.
Under optimal conditions (excellent lenses, oil immersion) the resolution of a light microscope is about 0.2 micrometers (or 0.000,000,2 meters or 2 thousandths of a millimeter). Objects that are closer together cannot be detected as separate. The resolution of an transmission electron microscope is about 0.05 nanometers (or 0.000,000,000,05 meters or half of 1 millionth of a millimeter). This means that the electron microscope has about 10,000 times the resolving power of the light instrument, and can therefore show far greater detail, for example of subcellular structure.
Another difference of importance to biologists is that light microscopes (there are several kinds, such as bright field and phase contrast) enable the viewer to watch living cells. The electron microscope produces an image of the shadows cast by atoms of heavy metals used as stains; the living tissue is destroyed by the intense beam of electrons.
Scanning electron micrograph (SEM) of various Pollen