The "virtual" particles are intended to avoid the "action at a distance" issue with fields. The virtual particles are place-holders for calculations.
They came about from looking at the philosophical problem of "What is a field"? A field between two interacting electrons changes the electrons trajectory.
OK... but what does it mean for the electrons to "interact"? Saying "there's a field" is just a circular argument.
The better response is "they exchange a photon". OK, but is the photon real? No... it's just a place-holder to make calculations easier.
Do two electrons actually exchange virtual photons? No one really knows... All we can say is that the theoretical calculations match the experimental ones. What that means is a question for philosophers. :)