a particle as an excitation of a field
Strike a guitar string and it hums at a definite pitch; pluck it harder and it sounds louder, but the pitch — the basic 'unit' of vibration — stays the same. Quantum field theory says elementary particles work the same way. Spread through all of space is an underlying field; an electron is a single quantized 'note' of the electron field, a photon is a single note of the electromagnetic field. The field is the instrument; the particle is one elementary unit of its vibration.
More precisely, each fundamental field can only hold energy in whole-number lumps — you can have one excitation, two, three, but never two-and-a-half. Each lump is a particle, carrying a fixed amount of energy, momentum, and other labels (charge, spin). Add energy to the field and you create more excitations (more particles); remove it and they vanish. This is why particles can be created and destroyed: a high-energy collision dumps energy into various fields and new ripples (new particles) appear, as long as the bookkeeping of energy and charge balances. It also explains why all electrons are perfectly identical — they are all excitations of the one and only electron field, so there is nothing to distinguish them.
This single idea quietly resolves several old puzzles. It is why matter can turn into energy and back (energy poured into a field becomes particles, per E = mc^2); why antiparticles exist (a field generally supports both a particle and its mirror-image antiparticle); and why the vacuum is not truly empty but a quiet field that can briefly flicker. A caveat worth keeping: 'excitation' is a precise technical notion only for free fields with definite energy; for strongly interacting fields the clean one-ripple-equals-one-particle picture gets blurry, which is part of why the strong force is so hard to compute.
In a particle collider, two protons smash together and out come dozens of particles that were not there before — pions, photons, the occasional heavy boson. None of them were hiding inside the protons; the collision energy excited various fields, and each new ripple is a new particle.
Collision energy poured into fields appears as a spray of brand-new particles.
A particle is not a tiny solid ball sitting on top of a field; it IS a quantized vibration of the field. The everyday word 'particle' is a convenient shorthand for something with no hard surface and no fixed location.