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

Employees dubbed it the Googleplex, a pun on the mathematical term googolplex, meaning an unthinkably large number.

If you don't know what 'googolplex' is, allow me to explain it to you.

If that's not mindboggling enough, a "googolplex" is a number with a googol number of zeros.

Cofounder Larry Page apparently misspelled the first half of "googolplex"  shorthand for a really big numberand, voila!

I think googolplex is good in Scrabble.

I was once charged a googolplex for a beer.

Sometimes the word “googolplex” was used generically to refer to an insanely large number.

These fluctuations could be happening every quadrillion years, or once every googolplex number of years.

Most of them would be different in size but some, similar to ours, would be far, far, far away, more than a googolplex meters away (or 10 to the power of 10 to the power of 100!).
Deepak Chopra: Hawking's Grand Book, But Where Is the Design? (Part 2)

Here's what's amazing about the Mac as it turns 25, a number that in computer years is just about a googolplex: It can look forward.
seanahan commented on the word googolplex
Actually, mathematically speaking, you can view this number as tiny. Now Skewes number, that's freaking huge.
February 26, 2008
thesuperiorbeing commented on the word googolplex
Why thank you, gangerh. And great pun!
February 24, 2008
gangerh commented on the word googolplex
Great googolplexplanation, TSB.
February 24, 2008
thesuperiorbeing commented on the word googolplex
You see, Googol is a number with one hundred zero's (you know, a million has 6 zero's a hundred has 2... well this one has 100). But Googolplex is a number with GOOGOL zero's. Also, if you tried to write googolplex down (the number, not the word),  even if each digit was the size of an ATOM  then it wouldn't fit inside the UNIVERSE. Impressive, eh?
February 23, 2008
oroboros commented on the word googolplex
10^{googol}
October 8, 2007