A googol is a huge quantity, 10 to the hundredth power (10100, or 1 followed by 100 zeros. The number was invented by Edward Kasner, an American mathematician, who popularized the number in his 1940 book, Mathematics and the Imagination. Though this number was not popularized until 1940, the term was originally coined in 1920, by Kasner's 9-year-old nephew, Milton Sirotta. At the same time, he also came up with the idea of a googolplex, which is one followed by a googol zeros.
The word has today been overshadowed by the household word Google, based on the search engine, whose name originated with a misspelling of googol. Like the even larger number googolplex, Google's headquarters in Mountain View is known as the Googleplex. Larry Page, one of the founders of Google, was fascinated by mathematics throughout life, and decided to name the company after the number.
When it was originally made up, a googol was the largest known number at the time. Today, there are numerous larger numbers, such as Graham's number or Skewes' number, whose analysis is made possible by supercomputers. A centillion, or 1 followed by 303 zeros, is another larger number. Of course, it is trivial for any mathematician to invent a number larger than these using arbitrary notion.
Although the googol number by itself has no mathematical significance, it is a nice reference point to use for visualizing other extremely larger numbers, such as the number of particles in the universe (about 1080) or the number of possible chess games (about 10130). 70!, or 70 factorial, which is 1x2x3... all the way up to 70, is only slightly more than a googol, with a value of about 1.2 x 10100. The prime factors of a the number have been determined, as well as those of other 100-digit numbers, thanks to modern-day computers.