When the Eagle turns its head towards the olive branch, that's a symbol of peace. Is there anything more specific you would like to know?
It's a Kennedy Half Dollar worth fifty cents. Looks like a small portion of the designers initials were polished off of the Die. Also had numerous circulation hits causing damage. Can you be more specific in that you see and are asking? Welcome to CT.
The eagles head is normally toward the eagles right (viewers left) because in heraldry, and most cultures, the right is the preferred or dominant side. You will sometimes see the nonsense written about the great seal of the US that "iIn times of war the eagles head is turned to its left facing the arrows of war." You will never find an image of the great seal, even from images made during times of war, that have the eagles head facing to its left. The head never turns. In proper heraldry the olive branch is placed in the eagles right talon to indicate a preference for peace (olive branch for peace in dominant right talon). Our early heraldic eagle coins were in error in a Heraldic sense as they have the arrows for war in the right or preferred talon.