In philosophy of language, a word's extension is the set of actual things to which it refers. So the extension of "father" is the set of all actual fathers. The extension of "basketball" is the set of all actual basketballs.
Notice there's more to a word than its extension. The word "father" isn't just a way of referring to a specific list of people who are now fathers; it also carries qualifications for being a father (or what it means to be a father). Whenever a person meets the qualifications for being a father, that person will now be part of the extension of "father."
Ever heard the expression, "six of one, half-dozen of the other?" We say this when what amounts to the same thing is being described two different ways. A philosopher might call these descriptions "extensionally equivalent," i.e. they both refer to the same set of actual things. So "housecat" and "felis catus" are two ways of referring to the same set of snooty furballs. "The Pole Star," "the North Star," and "Polaris" are three ways of referring to the same star. I suppose we could say "unicorns" and "fairies" are extensionally equivalent if there are no actual unicorns or fairies, which really goes to show there's more to a word than its extension! Philosophers call this other part of a word its intension. Notice the 's' which sets it apart from the more familiar word "intention."
The title of this blog has a similar breakdown. You can think of the extension as the "things" part of a word and the intension as the "ideas" part of a word.