Google (known as "Google!" during the 1990s) is a search engine that in many ways took over from Yahoo! as the dominant search engine (which in turn took over from Gopher). In the world wide web's short life, there have only ever been 3 search engines that have been the dominant search engines.
Unlike Yahoo and Gopher, Google relies on caches of web pages. In other words, Google will keep a track of what a web page once looked like, even if the page has changed in the meantime. When you search for something, Google will show you what the web page looked like at some time in the past. By doing this, Google can direct you to their own servers which have a copy of the web page rather than to the web page itself, thus saving time in searching. This is why Google is so much faster in coming up with results than Yahoo or the previous search engines ever were.
The down side to Google caching web pages is that it means that if you have said something in a web page that you regret or want to take down for some reason you can't because it is kept in the Google cache, at least for a few days. Thus if someone hacks your web site and posts up defamatory information, that information remains in the cache. This can be handy sometimes but just as often it is a real problem.
Another thing that Google does that its predecessors never did was that it lists web pages whether they like it or not. If you don't want to have your web page be searchable, bad luck. You cannot write to Google asking to be delisted, nor can you do anything to hide yourself from prying eyes. Google routinely ignores such requests, which was why Daniel Brandt set up Google Watch.
Google also has a formula for determining which sites get the most hits and hence which sites get to the top of the search lists. There are simple ways to rig it so that certain search terms end up with certain results being number 1 in the hit. Doing this is called a Google Bomb. For example, if you hate US president George W Bush and think that he is a thief for winning the election in spite of getting less votes, you can rig it so that anyone typing in "Thief" will have a web page on George W Bush as the number 1 hit. Even without deliberately making Google Bombs, it is clear that what is represented as the top hit often isn't actually the best site.
In addition to this, Google has also deliberately favoured Wikipedia entries on a topic, such that on any given topic a Wikipedia article is almost certain to be the number 1 hit on Google. This is based on some assumption that Wikipedia is more reliable than random web pages, a fallacy that has been proven with such examples as their truth-altering articles on serial comma and Port Arthur massacre, to name but 2. In return, Wikipedia favours Google, with many of their arguments to delete a Wikipedia article (or to keep it) being based on how many Google hits it gets.
Google also has a feature called "Ad Sense". Basically, it means that whatever is in your web site will attract advertisements from other sites on similar topics, and in turn your web site will appear on other web sites on similar topics. Anyone who clicks on those web sites and then buys things from either of you will get money. Thus installing Ad Sense is a way for web sites to earn income.
Ad Sense has been abused by people who scrape content from random sites, just so that they have some content and hence can make money. Some web sites are complete nonsense but end up with Google Ad Sense advertisements and make money from this.
Some sites also take advantage of Wikipedia's Copyleft agreement to scrape Wikipedia content, which looks like real arguments, so as to abuse Google Ad Sense. Thus a Wikipedia article can be copied 100s of times over, many of these copies being permanent because the scrapers don't need to ever change it. Thus if something is false in Wikipedia, it can remain false forever, even if changed in the Wikipedia copy. Whilst Wikipedia is very bad in their ability and willingness to change truth, even when they are doing the right thing, thanks to Google Ad Sense it doesn't matter much.
The word Google comes from the word "Googol" which is a mathematical term to mean 1 followed by 100 zeroes.
The headquarters of Google is called the "Googleplex" which is also based on a mathematical term, the "Googolplex", which means a 1 followed by a Googol zeroes.
Google used this term, known by mathematicians as the largest named number, so as to suggest that Google was very large, but not quite infinite.