Why are index funds called index funds?
Because they track an index.
Edited: The definition of the word in this case meaning "something used or serving to point out; a sign, token, or indication" from Meaning #3
I presume therefore you are asking what an index is?
There are many variations of what makes up an Index but in short it is a representation of some part of a market.
An extremely simplistic calculation would be to take a basket of stocks, and sum their prices. If one stock moves up a dollar, and one moves down a dollar, the index has effectively not changed, as it is presumed that the loss in one is offset by the gain in the other.