Translated from the Pali by Thanissaro Bhikkhu.
Provenance, terms and conditons
The uninstructed run-of-the-mill person
doesn't discern that as it actually is present,
which is why I tell you that
for the uninstructed run-of-the-mill person
there is no development of the mind."
The well-instructed disciple of the noble ones
discerns that as it actually is present,
which is why I tell you that
for the well-instructed disciple of the noble ones
there is development of the mind."
 This statement has engendered a great deal of controversy over the centuries. The commentary maintains that "mind" here refers to the bhavanga-citta, the momentary mental state between periods when the mental stream adverts to objects, but this statement raises more questions than it answers. There is no reference to the bhavanga-citta or the mental stream in any of the suttas (they appear first in an Abhidhamma treatise, the Patthana); and because the commentaries compare the bhavanga-citta to deep sleep, why is it called luminous? And why would the perception of its luminosity be a prerequisite for developing the mind? And further, if "mind" in this discourse means bhavanga-citta, what would it mean to develop the bhavanga-citta?
Another interpretation equates the luminosity of the mind with the "consciousness without feature," desribed as "luminous" in MN 49 and DN 11, but this interpretation also has problems. According to MN 49, that consciousness partakes of nothing in the describable world, not even the "Allness of the All," so how could it possibly be defiled? And, because it is not realized until the goal of the practice is reached, why would the perception of its luminosity be a prerequisite for developing the mind? And again, if "mind" here means consciousness without feature, how could the sutta talk of its development?
A more reasonable approach to understanding the statement can be derived from taking it in context: the luminous mind is the mind that the meditator is trying to develop. To perceive its luminosity means understanding that defilements such as greed, aversion, or delusion are not intrinsic to its nature, are not a necessary part of awareness. Without this understanding, it would be impossible to practice. With this understanding, however, one can make an effort to cut away existing defilements, leaving the mind in the stage that MN 24 calls "purity in terms of mind." This would correspond to the luminous level of concentration described in the standard simile for the fourth jhana: "And furthermore, with the abandoning of pleasure and pain as with the earlier disappearance of elation and distress he enters and remains in the fourth jhana: purity of equanimity and mindfulness, neither-pleasure-nor-pain. He sits, permeating the body with a pure, bright awareness. Just as if a man were sitting covered from head to foot with a white cloth so that there would be no part of his body to which the white cloth did not extend; even so, the monk sits, permeating the body with a pure, bright awareness. There is nothing of his entire body unpervaded by pure, bright awareness." From this state it is possible to develop the discernment that not only cuts away existing defilements but also uproots any potential for them to ever arise again. Only in the stages of Awakening that follow on those acts of discernment would "consciousness without feature" be realized.