I've heard this phrase a couple of times.
What is it?
It is your "Calling and election made sure"; "receiving the second comforter"; "The more sure word of prophecy".
Sometimes it is referred to as the second endowment. In the early days of the church, getting ones second endowment was quite common, and did not neccessarily carry with it the implications that it became known for later.
With the passage of time, the second endowment involved a couple receiving an invitation from a member of the twelve. From my understanding, part of the endowment took place in the temple, and the second portion, in the couples home. In the last portion they had the opportunity to "Seek the face of the lord", if they so wished, which was nothing less than a visitation from Christ himself.
That is what I recall from my days in middle earth, but I have to admit that it has been along time since I was in the shire....
I would say it has gone through a few evolutions, from Joseph Smith's ultra-secretive inner circle to Brigham Young and some of his successors giving it to almost everyone. A later prophet when they were attempting to crack down on polygamy understood that it was counterproductive to have a religious rite that guaranteed exaltation to polygamists, even when they were disobeying the law of the Church and the land, so it was minimized. The Buerger book has actual numbers of people who have received the ordinance in different periods if I remember right. The information dries up in the mid twentieth century though.
I think the implications originally were extremely profound. Joseph Smith did have a habit of promising people exaltation and that they would be saved for being loyal to him and doing things for him. The Second Anointing appears to be that in ritual form. The fact that it is in imitation of what the women did to Jesus shows one source for all the statements in the Journal of Discourses that Jesus was a polygamist, why else would these women have been performing a ritual reserved for wives??
I think now the LDS Church tries to downplay it as just "a special blessing", but I think that is for PR reasons, if they don't view it as being so important then why the level of secrecy that even family members aren't to be told that it exists or that the couple has received it.
Hasa Diga Eebowai