The electromagnetism acts between particles that are electrically charged. Its mediator particle is the photon. It mediates the information (momentum and energy) between charged particles. The photon itself has no charge, and it is also massless.
It is the exchange of photons between the negatively charged electrons and the positively charged atom nucleus that keeps the atom intact and determines its size. The small size of the atom is a result of that the electromagnetic interaction is relatively strong.