Using this phrase suggests you trust the recipient with sensitive information. I'm sending you the plan for your eyes only; it's critical that it stays between us.
Pro Tip 2/3
Serious Tone
Conveys a serious, urgent, or important tone, indicating the information is sensitive. Remember, the information I gave you is for your eyes only; please handle it with care.
Pro Tip 3/3
Expression Origin
Phrase originally implied top-secret documents in military or espionage contexts. The spy received a dossier that was for his eyes only and contained mission details.