Have you chosen one of the following options in the Set your settings button of your email list?
i) Activate Double Opt-in for this list but continue sending to all subscribers (Soft Double Opt-in)
ii) Activate Double Opt-in for this list and only send to verified subscribers (Strong Double Opt-in)
Then, when you click on the View all members button, you will notice that a new column has appeared which is named Double opt-in and the email address has the status Verified.
This means that this specific user has given you the consent via the Double Opt-in mechanism to send him Email Marketing newsletters.