It's a little easier to think about photons for starters, because we are more used to them. But it turns out that all the other particles in nature work this way ...
Start with a classical picture of a propagating electric field: a classical wave. Consider it in the context of a double-slit interference experiment. The electric field exists everywhere, at least everywhere we have any interest: after the source, between the source and the slits, within the slits, between the slits and the screen, at the screen. We can increase the intensity of the field as much or as little as we like. We have no trouble understanding this.
Add quantum mechanics: We no longer can change the intensity of the field in small amounts. We can only change it in quantum steps. When we raise the intensity by one quantum, we say that "we have created a photon". Lower the intensity by one quantum, and "we have destroyed one photon". Remember that the field exists throughout space. The "photon" has no specific location. Each time we create or destroy a photon we add or subtract a quantum of energy from the field. Not only that, we add or subtract momentum from the field. The field carries energy and momentum.
Suppose there is an atom in the field with energy levels whose energies differ by the energy of one quantum of the field. There's a chance (a probability) that the field will interact with the atom, in which case a photon will be destroyed, and the atom will take the energy and be raised to the higher energy state. It will also take the momentum from the field, and get a little kick in the direction of the field's momentum.
From the point of view of the atom, it looks like it's been hit by a particle. It has more energy, and has picked up some momentum. (Glossing over some conservation issues.) The interaction has occurred at the location of that atom. But the field excitation, the photon, lives everywhere in a pattern described by the classical wave. The field/wave obeys all the laws of wave physics, but the interactions happens at a particular location, and is indistinguishable from a particle collision. Wave and particle.
At the photographic film at the screen of the interference experiment, the field interacts with the molecules of the film at individual locations. But where those interactions might occur are determined by the law of interference.
It turns out that all elementary particles can be described by fields. So there are wave equations that tell us what the wavefunction is ... where interactions might occur. These fields are a little more complicated because of other conservation laws that apply in the subatomic domain: you can't destroy an electron as you can a photon, but you can redirect an electron, which is like destroying one electron and creating another that moves in a different direction. Or neutron can be destroyed while simultaneously creating and electron, proton, and neutrino. And so on.