The history of microscopy is an interesting one. More often than not, Anton van Leeuwenhoek is credited with inventing the first working microscope. Robert Hooke is the guy that coined the word "cell" from looking at a piece of cork with a microscope. Other biologists used microscopes to closer view plant and animal tissues. In sequential years, scientists stated that all plants are made from cells and then that all animals are made from cells.
Without microscopes, scientists would never have been able to examine living things in small enough detail to develop the modern day cell theory. Cell theory says that all living things are made of cells, all cells come from pre-existing cells, the cell is the simplest complete unit of living things.
Microscopes also led to the discovery of two completely new kingdoms in the classification of life--bacteria and protists. Without microscopes, thousands and thousands of living organisms would still remain unknown to us.
Without microscopes, cellular reproduction would still be a mystery. We would not have been able to view and witness things like binary fission, mitosis, meiosis, DNA synthesis, etc.
Microscopes have gone far beyond the capabilities of light microscopes. We now have scanning electron microscopes that bounce electrons off of matter. With that kind of magnification power, we have been able to see virus structures and DNA. Because of microscopes we have been able to understand how so much of life is built. We are seeing life at its building block level in order to better understand how the big organism works as a whole.