They are vibrations of quantum fields (in this case the electromagnetic field), so you can say that the fields are passing energy, momentum, angular momentum, etc from one place to another, and this "bucket brigade" of physical quantities is what we call a particle.

You could technically describe this as photons continuously being destroyed as they create new photons in adjacent locations. But it's not that physically meaningful, it's like adding +1 and -1 to the same side of an equation. It doesn't really do anything but use more ink.