The Quran

وَمَن لَم يَستَطِع مِنكُم طَولًا أَن يَنكِحَ المُحصَناتِ المُؤمِناتِ فَمِن ما مَلَكَت أَيمانُكُم مِن فَتَياتِكُمُ المُؤمِناتِ ۚ وَاللَّهُ أَعلَمُ بِإيمانِكُم ۚ بَعضُكُم مِن بَعضٍ ۚ فَانكِحوهُنَّ بِإِذنِ أَهلِهِنَّ وَآتوهُنَّ أُجورَهُنَّ بِالمَعروفِ مُحصَناتٍ غَيرَ مُسافِحاتٍ وَلا مُتَّخِذاتِ أَخدانٍ ۚ فَإِذا أُحصِنَّ فَإِن أَتَينَ بِفاحِشَةٍ فَعَلَيهِنَّ نِصفُ ما عَلَى المُحصَناتِ مِنَ العَذابِ ۚ ذٰلِكَ لِمَن خَشِيَ العَنَتَ مِنكُم ۚ وَأَن تَصبِروا خَيرٌ لَكُم ۗ وَاللَّهُ غَفورٌ رَحيمٌ

Muhammad Asad

And as for those of you who, owing to circumstances, are not in a position¹ to marry free believing women, [let them marry] believing maidens from among those whom you rightfully possess.² And God knows all about your faith; each one of you is an issue of the other.³ Marry them, then, with their people's leave, and give them their dowers in an equitable manner - they being women who give themselves in honest wedlock, not in fornication, nor as secret love-companions.⁴ And when they are married, and thereafter become guilty of immoral conduct, they shall be liable to half the penalty to which free married women are liable.⁵ This [permission to marry slave-girls applies] to those of you who fear lest they stumble into evil.⁶ But it is for your own good to persevere in patience [and to abstain from such marriages]: and God is much-forgiving, a dispenser of grace.

The phrase lam yastati tawlan is often taken to mean "he is not in a position to afford", i.e., in the financial sense; but Muhammad 'Abduh very convincingly expresses the view that it applies to all manner of preventive circumstances, be they of a material, personal or social nature (Manar V, 19).
In this context, ma malakat aymanukum (lit., "those whom your right hands possess") denotes women who were captured in a holy war and have subsequently embraced Islam. In the above phrase, the pronoun "you" refers to the community as a whole.
I.e., since all human beings - whatever their outward "social status" - are members of one and the same human family, and are therefore equal to one another in the sight of God (cf. 3:195), it is only the strength or weakness of faith which makes one person superior or inferior to another.
Lit., "and not taking unto themselves secret love-companions". This passage lays down in an unequivocal manner that sexual relations with female slaves are permitted only on the basis of marriage, and that in this respect there is no difference between them and free women; consequently, concubinage is ruled out.
The weaker social status of a slave makes her, obviously, more accessible to temptation than a free married woman is presumed to be.
I.e., to those who for one reason or another are unable to marry free women and are, at the same time, not equal to the temptations arising from celibacy. As is made clear in the next sentence, the Qur'an discourages such marriages - obviously with a view to removing a major attraction from the institution of slavery as such, and thus promoting its abolition.