The note from The Message of the Qur'an which is Muhammad Asad's translation:
"The best and simplest of these explanations is undoubtedly the one advanced by Ibnal-Qayyim (as quoted in Manar I,48): the term rahman circumscribes the quality of abounding grace inherent in, and inseparable from, the concept of God's Being, whereas rahim expresses the manifestation of that grace in, and its effect upon, His creation - in other words, an aspect of His activity."
He translates the phrase as:
In the name of God, most gracious, the dispenser of grace.
See also my first post on God's mercy and the third post on God's mercy.