The second epistle is addressed to an individual woman. One who had children, and a sister and nieces, is clearly indicated. According to one interpretation she is “the Lady Electa,” to another, “the elect Kyria,” to a third, “the elect Lady.” The object of St. John in writing the second epistle was to warn the lady to whom he wrote against abetting the teaching known as that of Basilides and his followers, by perhaps an undue kindness displayed by her toward the preachers of the false doctrine.
–Smith's Bible Dictionary