Matter can be divided in Newtonian:

Solid: can’t flow, can’t be compressed*

Liquid: can flow, can’t be compressed*

Gas: can flow and be compressed.

Fluid is anything that can flow, eg gases and liquids

Non Newtonian materials are generally man made materials that “cheat” and behave in a way not strictly in one of these groups. The most common are for example padding for body protections, a sort of rubber like material that can flex with your body but stiffens when hit. Very handy as it feels like clothing but protects like a solid pad. Another example is wet sand or mud, as a whole, it does not behave like a classic solid or a classic liquid.

*compressed in the sense that if you give infinite room, the gas will take all the room, and if you change the space it is confined, it will evenly be squeezed in it. Non compressible means that if you try compress the material, it will change its volume by very very little and oppose a lot of resistance to it.

These categories are broad and used for broad description. There are applications in which you can force these categories of material to do weird things, in extreme circumstances. For example, air at supersonic speed is not compressible, or better, does not behave like a compressible fluid.