I always thought that the phrase “First Lady” meant, by definition, the wife of the head of state; in particular, in the US, that it specifically meant the wife of the US President.
But during a visit to the Vermont Marble Museum a couple months ago, in a hall of busts of Presidents, I saw an explanatory card that mentioned that during Buchanan's Presidency, since he was unmarried, his niece Harriet Lane was the First Lady.
I couldn't figure out what that meant, since again I thought the definition of the term was “President's wife.”
But it turns out that the term has, at least sometimes, more generally been used to mean (among other things) “hostess of the White House”; and Ms. Lane is not the only unmarried woman to have served in that office.
In particular, the bit of that Wikipedia article that I find most surprising is the notion that Chelsea Clinton served as “Acting First Lady” during the two-week period between Hillary Clinton's swearing-in as Senator and Bill Clinton's leaving office as President.
But that's a contentious usage; the talk page for that article makes clear that some people vehemently disagree with it.
And nowhere else on the web is the phrase “Acting First Lady” applied to Chelsea Clinton. (Except other pages that quote the Wikipedia article; you can filter them out of a Google search by looking for pages that don't contain the unusual phrase “during the fortnight”.)
For example, a CNN article from August, 2000, implicitly distinguishes between the “first lady” (by whom they clearly mean Hillary Clinton) and the “first daughter [having] filled in” as hostess and as Bill Clinton's travel companion and source of moral support.
Still, regardless of the specific question of whether Chelsea Clinton can be said to have actually been a First Lady, it's nonetheless clear that the term has in the past, on occasion, been applied to women who were not married to the President.
By the way, the Wikipedia article on First Lady provides slightly more information about the use of the term outside of the US.