Vaguely means not clearly or precisely defined; something that's hard to describe exactly.
When people talk about something being vaguely related to their memory or idea, it usually means they can't quite put their finger on it. They might remember a face, but can't place where they saw it before - so it's only vaguely familiar. It's like trying to recall the name of that one actor in your favorite movie; you know they were famous, but the details are fuzzy. In conversations, people often use "vaguely" to describe something that's on the edge of their memory or understanding.
In a vague manner.
Example: He looked vaguely around the room, as if lost.
