Most large numbers are named by committees of mathematicians. A googol was named by a child.
A googol is 1 followed by 100 zeroes, or 10 to the power of 100. The word was popularized by Edward Kasner, an American mathematician, in the 1940 book Mathematics and the Imagination, which he wrote with James R. Newman. Etymonline lists that book as the first appearance in print. According to the book, Kasner asked his nephew to name a very large number, and the boy came up with "googol."
The boy was Milton Sirotta, who lived from 1911 to 1981. Wikipedia says the word was coined in 1920 when he was nine, which fits his birth year. Etymonline says only that Kasner reported the nephew as nine, or possibly eight, and gives no year. The 1920 date therefore rests on one reference source and should be treated as approximate.
A second term came at the same time. Etymonline says "googolplex" was coined in the same way, and that it means 10 raised to the power of a googol. It uses the suffix -plex.
The word has no deeper meaning. Etymonline notes only that it may have been influenced by Barney Google, a comic strip character of the era.
Googol is also bigger than anything physical. Wikipedia cites Carl Sagan's estimate of about 10^80 elementary particles in the observable universe. A googol is another 20 orders of magnitude beyond that. No physical count reaches it.
Its best-known descendant is a typo. David Koller's account at Stanford says that in September 1997 the graduate student Sean Anderson searched the domain registry for "google.com" instead of "googol.com" while checking a suggested name. The misspelled domain was free, and it was registered on September 15, 1997. Kasner's heirs reportedly considered legal action in 2004 over the name, according to Wikipedia, but none was filed. Since 2009 Google has used the domain 1e100.net, which is a googol written in scientific notation.