5 I ask you, how ye interpret what is said in the Gospel, “Let not your left hand know what your right hand does”? For if you understand this, you will discover what is your right hand, and what is your left: at the same time you will also understand that God made both hands, the left and the right; yet the left ought not to know what the right does. By our left hand is meant all that we have in a temporal way; by our right hand is meant, whatever our Lord promises us that is immutable and eternal. But if He who will give everlasting life, Himself also consoles our present life by these temporal blessings, He has Himself made our right hand and our left...
Source: The Enarrations, or Expositions, on the Psalms (New Advent)