Single opt-in method of signing up is the procedure of capturing the email address and name of the subscriber without directly taking the interest and the clear consent of the subscriber into account.  In other words, it would suffice if the visitor types their name and their email address and submit the form.  They will be added to the email list.  Hence it is called single opt-in.

On the other hand double opt-in method of signing up would want the visitor to go to their email box where they would have received an automated confirmation email wanting them to verify their email address, thereby giving their full consent to receive email notifications from you. 

Double opt-in method of capturing subscribers is a very safe and sure way of email marketing in the sense that you come to know that the subscriber is actually interested in receiving future communications from you.  Make the best use of well-designed forms to increase your subscriber count.