Fetching details from the dictionary...

to peel off; to come off; to flake off; to be worn off
to fade; to discolor; to discolour
「剥げる」 has another reading with different meanings.
壁のペンキが剥げてきたので塗り直す必要がある。
The paint on the wall is peeling, so it needs repainting.
古い家の壁のペンキが剥げた。
The paint on the old house's wall peeled off.
テーブルの表面の塗装が剥げている。
The finish on the table's surface is peeling off.