A speaker describes falling in love by looking into someone's eye and seeing the whole universe inside it. That's a big claim, and it captures the dizzy, all-consuming feeling of early love, when one person seems to hold everything. The speaker is sure of it, and assumes the feeling goes both ways: "I thought she felt the same."
The last line changes the tone. She says the speaker was her "world," but that she was the speaker's "galaxy." On the surface it sounds sweet, but a galaxy is far bigger than a world. Her words suggest the love isn't equal: she means less to him than he does to her, or at least she sees it that way. The past tense in "I thought" hints that the speaker has already realized this. The mood starts out wonder-filled and romantic, then turns quietly wistful, with a small sting of disappointment hidden inside a compliment.