Elect Lady-Title Defined

The title “Elect Lady” was applied to women on the Bible, on occasion, and in latter day prophecy through the Prophet Joseph Smith Jr.  What is the meaning?  Joseph Smith Jr wrote this of the title:

“I assisted in commencing the organization of ‘The Female Relief Society of Nauvoo’ in the Lodge Room. Sister Emma Smith, President, and Sister Elizabeth Ann Whitney and Sarah M. Cleveland, Counselors. I gave much instruction, read in the New Testament, and Book of Doctrine and Covenants, concerning the Elect Lady, and showed that the elect meant to be elected to a certain work, &c., and that the revelation was then fulfilled by Sister Emma’s election to the Presidency of the Society, she having previously been ordained to expound the Scriptures.”  History of the Church (LDS) 4:552–53