The COSMOLOGICAL CONSTANT is an extra term added by Einstein in working out equations in general relativity that describe the universe in the situation when it is "static", that is, not expanding. Remember that Einstein worked out the solutions before Hubble discovered that the universe was expanding.
In trying to solve the differential equations that describe space-time, Einstein needed to add a constant term to avoid having the universe collapse upon itself. This term balances the attractive force of gravity contributed by all of the matter in the universe. Physically, this term represents the "vacuum energy", the possibility that empty space possesses density and pressure, thus preventing the universe from collapsing.
When Hubble later showed that galaxies are moving away from us and hence, that the universe is expanding, this term was not longer necessary -- because the universe is not static. Einstein later felt that the inclusion of this term was the biggest blunder of his career, and in most models of cosmology made in the meantime, the cosmological constant dubbed "lambda" is assumed to be equal to zero.
Although the reason for Einstein's inclusion of the term is no longer valid, there remains the possiblity that the cosmological constant is not zero. There are two recent observational clues that suggest that Lambda is not zero:
Distant galaxies appear to be further away than their redshift would predict if the universe were not accelerating. These results arose from calculating the distances to galaxies that had supernovae in them.
The NASA WMAP lambda page
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