Loving the Elect Lady and Her Children

John the Elder begins his second letter with these words, "To the elect lady and her children, whom I love in truth, and not only I, but also all those who have known the truth, because of the truth which abides in us and will be with us forever: Grace, mercy, and peace will be with you from God the Father and from the Lord Jesus Christ, the Son of the Father, in truth and love." Who is this elect lady, who are who children and why and how are we, those who abide in the truth, called to love her?