In light microscopy it is the very nature of the visible light used that limits resolving power. Electron microscopes use radiation of much shorter wavelengths, namely electrons.
Early in the 20th Century electrons were shown to have wave properties and that the wavelength was governed by their velocity (the faster a beam of electrons, the shorter its wavelength). This discovery, plus the development of the magnetic lens (which is somewhat analogous to glass lenses used in light optical systems) were key advances in the development of the electron microscope.
Electron microscope magnetic lenses consist of a coil of wire shrouded in iron, which is continuous, but for a small gap in the lens bore. Transmission electron microscopes are constructed by stacking at least five of these lenses together to produce the electron optical column, with an electron source on top. The interior of the column is kept at high vacuum, because air molecules can impede the path of the electron beam. A specimen on a support grid is inserted into one of the magnetic lenses (the objective lens) and is imaged at high resolution.
The image produced can be further magnified and viewed on a fluorescent screen, or can be recorded on film, or on a CCD (Digital capture).