Second Season refers to the light novel series, not the anime
The word Second in the anime title Monogatari Series: Second Season is not based on the number of times the series has been animated (which is the usual practice), but rather based on the fact that the anime adapts the content from the Second Season of the Monogatari Series, which consists of 6 volumes (listed in order of publication): Nekomonogatari (White), Kabukimonogatari, Hanamonogatari, Otorimonogatari, Onimonogatari, and Koimonogatari.
The anime Monogatari Series: Second Season (summer 2013) has adapted (listed in airing order) Nekomonogatari (White), Kabukimonogatari, Otorimonogatari, Onimonogatari, Koimonogatari. And this summer (2014), Hanamonogatari will be animated under the title Monogatari Series: Second Season Hanamonogatari.
Earliest usage of the term
The term Second Season has been in used since mid 2011 in Monogatari Series article on Wikipedia.
It also has been used on an anime news site in March 2011, regarding the release of Hanamonogatari (emphasis mine).
How the term comes to use
As for why the 6 volumes are collectively called Second Season, according to Wikipedia article of Monogatari Series in Japanese:
My own translation1:
1 Feel free to edit in a correct translation.
Although the series was initially planned to end at Nekomonogatari (White), at which point the series have finished telling the story about Koyomi and all the people around him, Nishio Ishin was inspired by the anime adaptation of Bakemonogatari and announced the "Second Season".
The old version of the article noted the date of the announcement being June 2010.
Then, Bakemonogatari (2 volumes), Kizumonogatari, Nisemonogatari (2 volumes), Nekomonogatari (Black) are collectively called First Season for the sake of convenience after the Second Season was announced.
Unfortunately, the article (old or new) didn't cite any source regarding the announcement of the Second Season of the novel.