Zero point (insert physical term here) gets its name from the Heisenberg Uncertainty Principle, which dictates that an ideal harmonic oscillator -- one small enough to be subject to quantum laws -- can never be entirely at rest, since that would be a state of zero energy, which is forbidden.
Quantum electrodynamics predicts that a true vacuum creates virtual particles and waves that pop in and out of existence, also known as vacuum fluctuation or zero point fluctuation. Their lifetime is strictly limited by the uncertainty principle. This roiling quantum sea pervades all of the universe, even the empty space within atoms. Experimental evidence for the existence of zero point fluctuations are the Casimir Effect, the Lamb Shift, Van der Waals forces, diamagnetism, spontaneous emission, and microdegree liquid Helium. Zero Point Energy in and of itself has little or no meaning. However we can measure fluctuations in this "infinite" quantity when mass is introduced. In an article at the California Institute for Physics and Astrophysics, http://www.calphysics.org/zpe.html, they liken it to a boat floating on the ocean. The boat doesn't really care how deep the ocean is below it, just the changes that it can observe relative to it's position on the surface.
Sonoluminescence may also tap the Zero Point Energy. Dr. Claudia Eberlein in her paper "Sonoluminescence and QED" (Phys. Rev. Lett., 76, 3, 842, 10/96) describes her conclusion that only the Zero Point Energy spectrum matches the light emission spectrum of sonoluminescence, which therefore must be a Zero Point Energy phenomena. Philip Yam's article from Scientific American(12/97) continues the work of the late nobel prize winner Julian Schwinger and states,
"Basically the surface of the bubble is supposed to act as the Casimir force plates; as the bubble shrinks, it starts to exclude the bigger modes of the vacuum energy, which is converted to light."
Barber and Putterman discovered that sonoluminescent flashes only exist for 50 picoseconds or shorter. Atomic processes, on the other hand, emit light for at least several tenths of a nanosecond which leads many to apreciate Eberlein's proposal that Zero Point Energy is the source of the radiation.
For more information try Google and read this interesting paper at the Cornell arXiv: