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 the concealers (in battle), smite their necks until you have crushed them. Then bind your captives firmly. Thereafter set them free either by an act of grace, or against ransom. If Allah would do it, He would surely have made them pay for what they did. But He tests some of you by means of others. As for those who are slain in the way of Allah, He shall never let their works go to waste.” (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 one of the household in this period.
So, this expression is by no means an indication to slavery or concubinage.