My intuition for it is that there are fields at all points in spacetime (the fields of the standard model: a tiny vector of sorts), and excitations - certain patterns in these fields - behave as particles.
Combinations of excitations can be interpreted as different excitations, and by 'can be interpreted' I really mean "can spontaneously transmute into" according to the probabilities of quantum mechanics. Since all interactions occur in discrete units of these fields (except for the photon field), referring to these units as particles is a convenient and compelling approximation - but it doesn't tell the full story.
Basically, it very much seems that fields are the more fundamental concept.
Combinations of excitations can be interpreted as different excitations, and by 'can be interpreted' I really mean "can spontaneously transmute into" according to the probabilities of quantum mechanics. Since all interactions occur in discrete units of these fields (except for the photon field), referring to these units as particles is a convenient and compelling approximation - but it doesn't tell the full story.
Basically, it very much seems that fields are the more fundamental concept.