What is the meaning of "I am his hearing with which he hears and his sight with which he sees"?

The meaning of the Hadith is that whoever strives to draw closer to Allah through obligatory acts, then supererogatory ones, Allah will bring him closer and elevate him from the level of faith (Iman) to the level of excellence (Ihsan), so he worships Allah as if he sees Him. His heart becomes filled with the knowledge, love, and عظمه (magnificence) of Allah, which erases everything else from the heart. Nothing of the servant's self or desires remains. At that point, he speaks of nothing but Allah's remembrance and moves only by His command. If he speaks, he speaks by Allah; if he hears, he hears by Him; if he sees, he sees by Him; and if he strikes, he strikes by Him.

The meaning is not that Allah becomes the hearing itself, or the sight, or the hand, or the leg. Rather, it means that Allah guides and assists the person in his hearing, sight, striking, and walking, so he hears only what pleases Allah, looks only at what Allah loves, works with his hand only what pleases Allah, and walks only towards what pleases Allah.