A 'stretched out arm,' as in Exodus 6:6, signifies omnipotence or divine power, because 'an arm,' when stretched out in the heavens, represents power from the divine, but when not stretched out, but bended, it represents power in the general sense. This is why divine power is often shown in the Word as a stretched out arm or a strong hand.

(Verweise: Arcana Coelestia 7205)

It's common to say “I see” when we understand something. And indeed, “seeing” in the Bible represents grasping and understanding spiritual things. So it makes sense that the eyes, which allow us to see, represent the intellect, which allows us to understand spiritual things. This can also be used in the negative, of course; the Bible speaks of people having eyes and refusing to see, and the Lord when He was in the world advised plucking out an offending eye. These represent a refusal to acknowledge truth, or being misled by falsity.