Dark matter doesn’t actually exist. It’s just a tool for math.
First of all, there are two basic forms of dark matter. One is simply ordinary matter which isn't radiating enough light for us to detect it, or is too small for us to detect. The other, 'non-baryonic' dark matter, is believed to be some sort of strange exotic type of matter which doesn't interact with light and so is 'invisible' to our detectors. Both forms of dark matter are usually known of through their gravitational interactions with other objects. For example, the way in which the outer stars of many spiral galaxies move faster than expected as according to well established laws for orbiting objects (Kepler's 3rd Law, specifically).