I don’t know what particle are – no-one does! We know what properties they have and how they interact, but theories that try to explain what they actually are (e.g. tiny vibrating strings) are just speculation at the moment.
every particle can be though of as a small wave, or bump, or ripple on a field…like a magnetic or electric field. In fact a small ripple on the electric and magnetic field (they are alway together) is known as a photon or a particle of light. But it’s the same for every other particle. e.g. an electron is a ripple on the electron field.
There’s not much I could add to those explanations, but just picking up on what Tim wrote: if each particle is a ripple on some kind of a field, then that gives you a rough idea of why sometimes particles act really like point-like particles (because those ripples are in a specific place), and sometimes they behave like waves (because they are, even though the waves are only noticeable in a relatively small region of space). We can describe very well with mathematics what particles are and what they do, but we don’t really have proper words in our language for these kind of objects, because they are quite different from anything human beings can see and experience directly.