Question: What is the real meaning of "(people) that your right hands possess"? Does this mean that Islam allows for slave trade and allow men to exploit females that work in his house?
In Arabic, the term “ma malakat aymanukum” (ما ملكت أيمانكم) means “people under your guardianship”.
This includes 2 groups of people:
1- Adopted children (like orphans)
2- War captives
Both of these groups can only stay temporarily under one’s guardianship.
As for the adopted children, Allah commands:
“Test the orphans until they reach the marriageable age. Then if you perceive in them sound judgment, release their property to them. Do not consume their property excessively and quickly, for that they will grow up and take it back. The rich should behave honestly (by not spending their wealth), and the poor should consume only as much as what is fair. Bring witnesses when you release their property to them. Allah is sufficient to call to account.” (An-Nisa/ The Women 4:6)
As for the war captives, Allah commands:
“When you meet those deniers (in battle), smite their necks until you suppress them. Then cordon (the rest of) them off strictly; thereafter set them (the captives) free, either by an act of grace or against ransom. Do this, so that the burden of war is laid down.” (Muhammad 47:4)
These two types of people have some limited time to spend with their guardians. They are to be taken to homes and treated like a person of that household in this period.
So, this expression is by no means an indication of slavery or concubinage.