In the case of e-mail, relevancy is the intellectual equivalent of value to the audience. An offer in and of itself has no relevancy. Even if I said I had free gold for you, unless I somehow magically attached it to the e-mail, it would have no relevancy. Relevancy is content that relates to the intended targets life or job. Industry news is relevant if it's news.
Entertainment can be relevant if the target is, in fact, entertained.
The key to relevancy is in the audience. Opting in is a way for your audience to confirm relevancy. Opting in is the process of your customers identifying themselves as wanting information from you. Staying relevant means keeping value in the communications you send. Whether it's a valuable offer, industry news, or a great song, it has to be valued in the eyes and minds of the recipient.