A bodhisattva―protector of monasteries, depicted as shading his eyes with his hand and looking afar, said to have been a Warden of the Coast under the emperor Aśoka.

A Dictionary of Chinese Buddhist Terms, William Edward Soothill and Lewis Hodous

（菩薩）護伽藍神之一。右手加額為遠望勢之像是也。原為大唐阿育王山之鎮守，修利或作修理者非是。育王山臨東海，渡海者每望山祈船中安全，以其手加額者，遙望其船而保護之之意，其證為月江印禪師之育王錄曰：「僧問：大權菩薩因甚以手加頞？師云：行船全在樞稍人。」

丁福保《佛學大辭典》