From Mathematics and the Imagination:
"Words of wisdom are spoken by children at least as often as by scientists. The name "googol" was invented by a child (Dr. Kasner's nine-year-old nephew) who was asked to think up a name for a very big number, namely, 1 with a hundred zeros after it. He was very certain that this number was not infinite, and therefore equally certain that it had to have a name. At the same time that he suggested "googol" he gave a name for a still larger number: "Googolplex." A googolplex is much larger than a googol, but is still finite, as the inventor of the name was quick to point out. It was suggested that a googolplex should be 1, followed by writing zeros until you get tired. This is a description of what would happen if one actually tried to write a googolplex, but different people get tired at different times and it would never do to have Carnera a better mathematician than Dr. Einstein, simply because he had more endurance. The googolplex then, is a specific finite number, with so many zeros after the 1 that the number is a googol [i.e., not 100 zeros after the 1, but a googol of zeros after 1.] A googolplex is much bigger than a googol. 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."
ETA: It is said that the Google search engine was based on a misspelling of Googol:
"Sean and Larry were in their office, using the whiteboard, trying to think up a good name - something that related to the indexing of an immense amount of data. Sean verbally suggested the word "googolplex," and Larry responded verbally with the shortened form, "googol" (both words refer to specific large numbers). Sean was seated at his computer terminal, so he executed a search of the Internet domain name registry database to see if the newly suggested name was still available for registration and use. Sean is not an infallible speller, and he made the mistake of searching for the name spelled as "google.com," which he found to be available. Larry liked the name, and within hours he took the step of registering the name "google.com" for himself and Sergey (the domain name registration record dates from September 15, 1997)."