Physicist: Short questions are real killers!
“Mass”, like practically everything in physics, is defined in terms of its properties, like:
1) Mass has inertia.
2) Mass creates gravity (energy does this too).
3) Mass travels slower than the speed of light.
Anything with these properties has mass. But as for what mass is: no idea.
I’ve heard theories about mass being “knots” of spacetime, but the most promising theory today involves the Higgs field. Essentially it describes “a field” that imparts the properties of mass to most types of particles (not photons, for example).
But that’s not much closer to an answer.
I suppose it’s best to say that there are a lot of things in this universe with a certain set of properties in common, and we say that those things “have mass”.
I do recognize how deeply disappointing that answer is. I mean “mass is something with the properties of mass”? What the hell are you supposed to do with that?
You could make the argument that it’s impossible to really understand what anything is, and that what we consider “intuitive understanding” is nothing more than a familiarity with a some set of familiar properties. If you wanted to make that argument anyway.
Even electrons, which today we know are some kind of especially small particle thing, were named long before their size or particleness were known. They were named for the fact that when you rub amber with fur, the amber acquires some strange properties (a negative electric charge), and the thing that causes those properties came to be known as “electron”, the Greek name for amber.
Point is, the name was given to a set of properties, and at the end of the day that’s probably the case for damn near every thing worth naming.
This kind of crappy answer isn’t restricted to physics, by the way. You want to waste an evening; get a biologist or zoologist drunk and ask them, “Hey, what’s a species?”.