It would help if you gave more context. It can mean idealism, worshipful, naïve, overcome by awe. It often is used disparagingly: someone is too idealistic, too worshipful, too naïve.
The "starry-eyed" person has their eyes wide open, staring in awe at something. I'm not sure if the literal idea is that they are gazing as if at the stars, or whether it means the reflections in their eye look liked stars.
Adolescents and young adults can become starry-eyed about a person, a performer, a politician or a political movement. As they grow older and more experienced, they become more cynical and down-to-earth.
"Then she snatched up the paper. Yes, she had passed—there was her name at the very top of a list of two hundred! That moment was worth living for. 'You did just splendidly, Anne,' puffed Diana, recovering sufficiently to sit up and speak, for Anne, starry eyed and rapt, had not uttered a word. 'I’m just dazzled inside,' said Anne."
"There was always a small corps of starry-eyed adolescents who found the whole improbable saga entirely believable, or at least half believed it might be partly true."