From what little we do know, it seems that the slave bracelet enhances and facilitates the Psys ability to control his Gift.
There are also different types of slave bracelets, and we don't really know what all the different types do. We know, for instance, that some can cloud memory of events prior to the slave taken on the bracelet. The bracelet also allows a Master to punish and kill his slave, and it also prevents the slave from escaping or disobeying direct orders.