I guess you know about electromagnetic fields. We can send light through a double slit and confirm that it indeed behaves like a field. Sometimes, those fields behave like particles (e.g. gamma radiation), called photons. The double slit experiment works with matter particles as well - we probably need the same framework for them. The description has to cover field-like and particle-like behavior, it has to be consistent with special relativity, and it has to explain interactions between different things. The answer is quantum field theory.
In quantum field theory, the fields are the fundamental concepts. We have a field for electromagnetism. We have a field for electrons and positrons (or two, depending on how you count, but that is irrelevant here). We have a field for muons and antimuons. And so on. Particles are a bit like waves in those fields, traveling through space. Don't take that analogy too far.