Second

A second was a unit of time measurement. Though not the smallest such unit, it was still most useful for measuring only short spans of time. According to the Fourth Doctor, 2,678,400 seconds were in a month. (TV: The Brain of Morbius)

A galactic second was used by the Daleks. (COMIC: Return of the Daleks)

According to the Second Doctor, the normal range of human blinking was about once every ten or fifteen seconds. Observing that Tobias Vaughn blinked far less frequently than that, the Doctor found him to be inhuman. Indeed, Vaughn was actually a cyborg. (TV: The Invasion)

Via a temporal pocket, locations and items could be put a second out of sync with the rest of N-Space. During the 2009 Sontaran invasion of Earth, the Sontarans hid the true nature of ATMOS via such a method. (TV: The Sontaran Stratagem) The New Dalek Empire used the same method to the stolen planets, making the Medusa Cascade, their staging area, look empty. (TV: The Stolen Earth) Shortly before his regeneration, the Tenth Doctor put his TARDIS a second out of sync to prevent from stealing it. (TV: The End of Time)

The technology that drove the Foretold meant that it had to wait sixty-six seconds after appearing to its victim before killing them. (TV: Mummy on the Orient Express)

Behind the scenes
Although the Doctor doesn't specify, it seems logical to assume that he is speaking of months as measured on Earth, since he's talking to Sarah Jane Smith, a human. In fact, the Doctor's maths is precisely correct for a 31-day month.