What is it? We're not sure. We can't see it or touch it. (IOW, it doesn't interact with the EM spectrum.) Yet we know it's there.
How? By its gravitational influence on baryonic matter and light.
It was discovered when scientists (such as Lord Kelvin and Fritz Zwicky) tried to work out how gravity affected stuff around it. What they could see and what gravity told them was out there, were two different things. Over and over, they worked the calculations and came up with gravity telling them there was more out there than first thought.
But what could it be? Until we figure it out, we've called it dark matter. There's a few guesses using ideas involving acronyms such as MACHO and RAMBO and WIMP.
Now, some hypotheses suggest that our understanding of gravity might not be fully correct. That's a possibility. But until we can come up with a better one, we'll take the one we've got and try to account for the strangeness.
Dark matter comes in cold, warm and hot, (references to its velocity, not it's actual temperature). After all, if we could detect its temperature, it would be interacting with the Electromagnetic Spectrum and would therefore not be Dark Matter. There's also Dark Energy, which is believed to drive the expansion of the universe.
So, make any sense? Don't worry if it doesn't. But if your brain hasn't fried yet, consider this little possibility: could there be some sort of connection between dark matter and Fermi's paradox?
Go hardcore: see how Dark Matter affects the universe as we know it.
Ever wonder if there was something out there that we simply couldn't see?
Her Grace refuses to lose sleep over something she can't see.