In quantum field theory, the fact that the particle number operator does not commute with the Hamiltonian implies the number of particless in an area of space is not a well-defined quantity, but like other quantum observables is represented by a probability distribution. Since these particles do not have a permanent existence, they are called virtual particles or vacuum fluctuations of vacuum energy.
Even though we can't see them, we know that these virtual particles are "really there" in empty space because they leave a detectable trace of their activities. One effect of virtual photons, for example, is to produce a tiny shift in the energy levels of atoms. They also cause an equally tiny change in the magnetic moment of electrons. These minute but significant alterations have been very accurately measured using spectroscopic techniques. The Casimir effect is an attraction between two uncharged parallel metal plates because fewer virtual particles can be created between the plates than in the surrounding space.
Virtual particles are always created as a particle-antiparticle pair, and mutually annihilate in short order. In some cases, however, it is possible to boost the pair apart using external energy so that they avoid annihilation and become real particles. This is the process by which black holes evaporate.
Examining normal physical processes with knowledge of this particle - antiparticle phenomena can lead to interesting insights such as quantum electrodynamics.