To dream of an apron represents commitment, or a willingness to do whatever it takes to think, feel, or act in a certain way. You or some aspect of your personality is very focused and willing to endure sacrifices to stay focused and on task. You may not care how messy or difficult it gets.
An apron suggests a strong interest in what you are thinking and maintaining it. Secrecy, over-protection, or sacrificing less important or interesting things to keep thinking in a certain way.