Virtual Particles are hypothesized units that are used in order to describe the Feynman lines. These "lines" are mathematical equations that describe, for example, a neutron decaying into a proton, electron and anti-neutrino. The stages between the neutron and the subsequent particles are said to be filled by these so-called virtual particles.
Virtual particles can never be detected. This is because they are theorized to spontaneously "pop" up all over the universe. This would not violate the conservation of mass and energy law because at the instant these virtual particles appear, they disappear, so they cannot be detected. This, however, means that it would be very difficult to prove their existence, if possible altogether. Virtual particles are thought to play important roles in the electromagnetic radiation of black holes, which is explained in another article.