Definitions
from The American Heritage® Dictionary of the English Language, 4th Edition
 n. The number 10 raised to the power 100 (10100), written out as the numeral 1 followed by 100 zeros.
from Wiktionary, Creative Commons Attribution/ShareAlike License
 n. The number 10100, written as 1 followed by 100 zeros.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 n. a cardinal number represented as 1 followed by 100 zeros (ten raised to the power of a hundred)
Etymologies
Examples

June 30th, 2008 at 10: 32 am googol is 1 followed by 100 zeros. gladyz Says:

Famously, Page and Brin rented a garage as their startup home and, on September 4, 1998, launched Google Inc, a deliberate misspelling of the word googol, the mathematical term for a one followed by a hundred zeros.

In a nod to their geeky roots as children of computer science and math professors, Page and Brin had derived the name from the mathematical term "googol"  a 1 followed by 100 zeros.

First off, they specifically took the name of the company from the word googol, which is a very large number 1 with one hundred zeros after it, after first thinking of the word googolplex, which is 1 followed by a googol of zeros, as a symbol of the immense amount of data their search engine would search through.
Comic Book Urban Legends Revealed #155  Comics Should Be Good! @ Comic Book Resources

The name itself springs from a number—a googol is a 1 followed by 100 zeros.

Even more impressive is a googol, which is greater than the number of particles in the known universe:

Google probably wanted to use 10e100, since that character string means 10 to the 100 power  in other words, a googol.
Search Engine Optimization and Marketing News provided by Cumbrowski.com

A googol is a one followed by a hundred zeros  or, in technical terms, "a freakin 'ginormous number."

This number, called a googol (just a madeup name), is the largest number with a name.

The company name is a play on the word googol, which refers to the number 1 followed by one hundred zeros.
marco_nj commented on the word googol
Choosing to name the company, 'Google' rather than Googol?
January 18, 2009
rolig commented on the word googol
What was deliberate, Marco?
January 17, 2009
marco_nj commented on the word googol
When spelled correctly, it looks more evil, almost Tolkienish (next to Gorgoroth?), which of course would go against Google's "Do no Evil" credo. I'm sure this was deliberate.
January 17, 2009
palooka commented on the word googol
How about a googolplex? Googol is the numeral 1 followed by 100 zeros, or 10 raised to the power of 100. A googolplex is 10 raised to the power of a googol! That's a lot of damn zeros.
January 6, 2007
mager commented on the word googol
not many people know what a googol is :)
January 6, 2007