If something happens noticeably, you can see it or feel it without trying hard — the change is easy to notice. It is the how-word from noticeable: she is noticeably taller; the room is noticeably quieter; he has improved noticeably. People use it a lot with words like better, worse, bigger, and with verbs like change, improve, increase. It is ordinary English, a little more careful than you can tell, and you will hear it from teachers, doctors, and newsreaders. Though actually, it does not have to mean a huge change. A noticeably different haircut can still be a small one; the point is that other people can spot it. If nobody would see the difference, you would not say noticeably. It is not a word for famous or special — only for “you can tell”.