BTW here is an excellent simple easy for anyone to understand explanation:
The Quantum Expectation
The equations of quantum field theory describing interacting particles and anti-particles of mass M are very hard to solve exactly. With a large amount of mathematical work it is possible to prove that the ground state of this system has an energy that is less than infinity. But there is no obvious reason why the energy of this ground state should be zero. One expects roughly one particle in every volume equal to the Compton wavelength of the particle cubed, which gives a vacuum density of
rho(vacuum) = M4c3/h3 = 10^13 [M/proton mass]4 gm/cc
For the highest reasonable elementary particle mass, the Planck mass of 20 micrograms, this density is more than 10^91 gm/cc. So there must be a suppression mechanism at work now that reduces the vacuum energy density by at least 120 orders of magnitude.
http://www.astro.ucla.edu/~wright/cosmo_constant.html