They seem to be mathematical assumptions in order to allow a "force" to move from one physical location to another physical location. The assumption is that gravity, for instance, moves from one particle of mass to another because in-between those particles is a series of virtual particles (in this case, bosons) which "transfers" the force from one location to another. (Note in this explanation the force itself is only a state of the background energy field partially coalescing in a particular location, with trade-offs between temporal duration, mass, velocity and angular momentum supposedly able to allow for conservation of energy and angular momentum, in most cases). The particle is said to be virtual because it is only a partial manifestation of the background field from which the particles themselves came. Thus when virtual particles form they are short-lived, and are like "waves" of a broader energetic field that is propagating a force from here to there.
The assumption of virtual particles is needed to make the math work out, apparently, to transfer potential energy around, and quantum field theory is able to supply the basis for claiming that such mathematical postulates are reflections of reality itself (as QFT claims that QM probability waves do not literally exist but are only "mathematical functions", it becomes much easier to reify one's math terms as "the reality itself").
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