Its mentioned in several ahadith (like this) that the 'wala' of a slave is for the one who buys the slave, and that 'wala' should not be bought and sold.
This 'wala' comes up a lot in the ahadith concerning slavery.
What does it mean ?
In short wala in Arabic means loyalty.
Why is it so important?
Wala is one of the conditions of Iman. Allah has stated:
And if they had believed in Allah and the Prophet and in what was revealed to him, they would not have taken them as allies; but many of them are defiantly disobedient.﴾٨١﴿
It is not just for slaves, you will find many Ahadith that shows that loyality to Allah should never be bought or sold as it is one of the basics of islam.
The word wala in your question's context has a legal meaning that comes with rights and duties. Therefore there is no direct translation.
The meaning has elements of similar yet different concepts. Among others you find in it the notions of:
- guardianship, custodianship, wardship
- tutelage, trusteeship, curatorship, fosterage
- maybe there are other nuances