River: "You know when you see a photograph of someone you know, but it's from years before you knew them. and it's like they're not quite finished. They're not done yet. Well, yes, the Doctor's here. [...] But not my Doctor. Now my Doctor, I've seen whole armies turn and run away. And he'd just swagger off back to his Tardis and open the doors with a snap of his fingers."
River is referring to his mental age. Even while being immortal the Doctor ages. It's like seeing the difference between someone from the age of 19 to 20, even though you can't always see physical changes their demeanor and attitude will change. She was likely referring to him in that way. In other concepts the eyes are often used to see one's age, in example, 'seeing the weariness in someone's eyes' she could be seeing him without the same burden that he will eventually carry, because he definitely ends up shouldering a lot of burdens in the later seasons. Being that she is his wife she would see those kind of changes and recognize them. Basically she isn't referring to physical age per se, likely multiple different factors.