Here "heart" is a metonym for a person's mind. The phrase "eyes of your heart" is a metaphor for one's ability to gain understanding. Alternate translation: "that you may gain understanding and be enlightened" (See: [[rc://en/ta/man/jit/figs-metonymy]] and [[rc://en/ta/man/jit/figs-metaphor]])
This may be stated in the active tense. Alternate translation: that God may enlighten your heart" or "that God may enlighten your understanding" (See: [[rc://en/ta/man/jit/figs-activepassive]])
Here "the hope" refers to what God wants us to confidently expect. Alternate translation: "what he has called you to confidently expect" or "what he has called you to confidently wait for"
What God has promised and will provide is spoken of as though it were property or wealth that one would inherit from a family member. Alternate translation: "the riches of all the glorious things he has promised to give to all God's holy people" (See: [[rc://en/ta/man/jit/figs-metaphor]])