JC - Chapter 33

As the Savior introduced the ordinance of washing as He washed His apostle's feet, Peter protested -

"...Lord, dost thou wash my feet?..."  (New Testament | John 13:6)

The Savior taught -

"...What I do thou knowest not now; but thou shalt know hereafter."  (New Testament | John 13:7)

Even -

"...If I wash thee not, thou hast no part with me."  (New Testament | John 13:8)

I personally interpret that to mean that in order to become part of Him or be linked or sealed to the family of Israel throughout eternity, besides baptism we must receive the ordinance of washing.

In modern day, the ordinance of washing was introduced to members of the school of the Prophets where -

"...ye shall not receive any among you into this school save he is clean from the blood of this generation;
139 And he shall be received by the ordinance of the washing of feet, for unto this end was the ordinance of the washing of feet instituted.
140 And again, the ordinance of washing feet is to be administered by the president, or presiding elder of the church."  (Doctrine and Covenants | Section 88:138 - 140)

Obviously, the purpose of washing is to be "clean from the blood of this generation".  Of washings we were later instructed -

"...verily I say unto you, how shall your washings be acceptable unto me, except ye perform them in a house which you have built to my name?
38 For, for this cause I commanded Moses that he should build a tabernacle, that they should bear it with them in the wilderness, and to build a house in the land of promise, that those ordinances might be revealed which had been hid from before the world was.
39 Therefore, verily I say unto you, that your anointings, and your washings, and your baptisms for the dead, and your solemn assemblies, and your memorials for your sacrifices by the sons of Levi, and for your oracles in your most holy places wherein you receive conversations, and your statutes and judgments, for the beginning of the revelations and foundation of Zion, and for the glory, honor, and endowment of all her municipals, are ordained by the ordinance of my holy house, which my people are always commanded to build unto my holy name."  (Doctrine and Covenants | Section 124:37 - 39)

The ordinance of washings then in our day are to be administered in holy temples.