A light microscope passes light through a thin specimen and uses lenses to magnify it. It can show the nucleus, cytoplasm, cell wall and chloroplasts of cells. But it cannot show very small structures clearly, because its resolution is limited. Resolution is the ability to see two points close together as separate points. Ribosomes cannot be seen with a light microscope at all, and mitochondria appear only as tiny blurry shapes.
Electron microscopes were developed in the 20th century. They use a beam of electrons instead of light. Electrons have a much shorter wavelength than light, so an electron microscope has a much higher resolution and a much higher magnification. Transmission electron microscopes show thin slices of the inside of cells, and scanning electron microscopes show the surface of a specimen.
Using electron microscopes, scientists could see ribosomes, the folded inner structure of mitochondria and the detail of the cell membrane and plasmids. Seeing this extra detail helped them to understand the role of each sub-cellular structure, for example that ribosomes are the site of protein synthesis. Electron microscopes are expensive and large, and specimens must be dead, so light microscopes are still used to observe living cells.