D&C 88

The Merriam-Webster dictionary defines sanctify as -

1)  to set apart to a sacred purpose or to religious use - consecrate, and

2)  to free from sin  - purify

In revelation, the Lord explained -

"...if your eye be single to my glory, your whole bodies shall be filled with light, and there shall be no darkness in you; and that body which is filled with light comprehendeth all things."  (Doctrine and Covenants  Section 88:67)

In then He provides what He means by sanctify -

"Therefore, sanctify yourselves that your minds become single to God, and the days will come that you shall see him; for he will unveil his face unto you, and it shall be in his own time, and in his own way, and according to his own will."  (Doctrine and Covenants Section 88:68)

I then interpret His commandment to mean that  to sanctify ourselves, we must turn our eyes and thoughts such that they are always single to God's glory, not our own.  That all things are done according to His will and wise purposes.  Wherein is the challenge to do all things with God's glory in mind.  The Savior was the great exemplar of this as He declared -

"I can of mine own self do nothing: as I hear, I judge: and my judgment is just; because I seek not mine own will, but the will of the Father which hath sent me."  (New Testament John 5:30)