Using all 7 tiles nets a Scrabble player a 50-point bonus and is sometimes referred to as a "Bingo". I'm curious: how did that term come into use and why does it have such meaning?
There is a good detail on Scrabble Bingo's on the Wikipedia page here.
Bingo is a game where each player is issued a card with numbers. A caller calls out numbers drawn at random and the player will cross of numbers on their card. The first person to have all of their numbers crossed off will shout out Bingo! So there is a parallel between this game where all of the numbers have been marked on the card and using all of your tiles in Scrabble.
You can read more about the game Bingo on its wiki page. Note the wiki page mentions that game has its earliest recording in 1776. It is my assumption it was long popular before Scrabble and that is why the term was borrowed for Scrabble because of the parallel mentioned above.
I checked the Online Etymology Dictionary and it says the origin of the phrase is unclear.
If you want to know more about the word itself you should try asking as a separate question on http://english.stackexchange.com/
As xiaohouzi (little monkey?) said, "bingo" comes from the game of Bingo. According to the Oxford English Dictionary, the word "bingo" comes from the word "bing" for a pile of something. In this case, presumably, it would be a pile of coins that you win for getting the right pattern on your card. The word "bing" is an old-fashioned word but still in use in northern England. Here's an example from Robert Burns's poem, The Brigs of Ayr. Robert Burns is a well-known Scottish poet.