A googol is 10¹⁰⁰ (which is 1 followed by 100 zeros). The term was invented by Milton Sirotta, the 9-year nephew of mathematician Edward Kasner, who had asked his nephew what he thought such a large number should be called. Such a number, Milton apparently replied after a short thought, could only be called something as silly as...a googol! A googol is larger than the number of elementary particles in the universe, which amount to only 10 to the 80th power.
Later, another mathematician devised the term googolplex for 10 to the power of googol,
that is,10¹⁰¹⁰⁰. Pronunciation in English.
Frank Pilhofer has determined that, given Moore's Law (which is that computer processor power doubles about every 1 to 2 years), it would make no sense to try to print out a googolplex for another 524 years - since all earlier attempts to print a googolplex out would be overtaken by the faster processor.

A googolplex is much bigger than a googol, much bigger even than a googol times a googol. A googol times a googol would be 1 with 200 zeros, whereas a googolplex is 1 with a googol of zeros. You will get some idea of the size of this very large but finite number from the fact that there would not be enough room to write it, if you went to the farthest star, touring all the nebulae and putting down zeros every inch of the way.

More big numbers

Link to a nice big number-homepage