D&C 107

The Lord differentiates -

"The power and authority of the higher, or Melchizedek Priesthood, is to hold the keys of all the spiritual blessings of the church—
19 To have the privilege of receiving the mysteries of the kingdom of heaven, to have the heavens opened unto them, to commune with the general assembly and church of the Firstborn, and to enjoy the communion and presence of God the Father, and Jesus the mediator of the new covenant.
20 The power and authority of the lesser, or Aaronic Priesthood, is to hold the keys of the ministering of angels, and to administer in outward ordinances, the letter of the gospel, the baptism of repentance for the remission of sins, agreeable to the covenants and commandments."  (Doctrine and Covenants | Section 107:18 - 20)

In my mind, "spiritual blessings" is that which comes by the power and authority of the Holy Ghost.  It is by the power and authority of the Melchizedek Priesthood that we are given to receive the Holy Ghost.