A particle is just an excitation in some quantum field. These fields permeate all space and are coupled to each other. As one of these excitations evolves in time, it can take any number of paths. The probability amplitude for a particle to be at some location after some amount of time is the sum of all the possible paths the particle could have taken to get there, weighted by a factor which makes out of the way paths less likely.
Because the fields that the particles are made of are coupled to each other, some of these paths "go through" another type of field and thus another type of particle. For example, one possible path for a photon has it split into an electron and a positron that then recombine into a photon. An electron can emit a photon, that photon can become a bunch of quarks, the quarks can recombine into the photon and the photon can then recombine with the electron. In this sense, any particle is made up of all particles as it moves through time.