Why were the religious leaders able to understand the Psalms when Stephen spoke?
They knew their Old Testament, especially the Psalms, which they sang in worship and knew as well as their own names. That deep familiarity allowed them to grasp the significance when Stephen spoke of seeing Him standing at God's right hand, and it aroused their anger.
Les explains that the religious leaders were steeped in the Old Testament, especially the Psalms, because they sang them in worship and knew them like their own names. So when Stephen declared that he saw Him standing at the right hand of God, the leaders understood the connection to Psalms 67 and 68. Les says this may not be the exact answer, but it is the explanation he is comfortable with: something attached to Stephen seeing Him standing aroused their anger. Israel had not forgotten Peter's earlier preaching that God raised Jesus from the dead and He could still be their King.