Double opt in simply means you need to confirm your email address after the initial submission.

This site (savvysme.com.au) runs a double opt in process, after you sign up you receive an email with a link in it that you need to click through to activate your membership.

It confirms that the owner of the email address that is being subscribed actually belongs to the person subscribing.

Following up on Anne's point, the Australian Spam Act allows electronic marketing messages (ie usually email but increasingly SMS as well) to anyone who has explicitly or implicitly given you their permission.  Check out the details at http://www.acma.gov.au/Industry/Marketers/Anti-Spam/Ensuring-you-dont-spam/key-elements-of-the-spam-act-ensuring-you-dont-spam-i-acma

Double opt-in is explicit permission so leaves no doubt that you are Spam Act compliant.  However, the double opt-in process does usually result in lower sign-up rates.  The challenge is to build as big a list as possible without spamming or annoying people.  (Spamming is illegal, annoying people is bad business practice!)

Rule of thumb - if you're using external lists, go for double opt-in.  If you're communicating with actual current customers, you're probably safe without an opt-in - being a customer is a fairly strong implied permission to market to them.

The grey area comes with random email addresses you have collected at business events, over meetings and so on.  Do you have permission or not? 

If you have a backlog of these, try sending everyone an email saying 'we have your contact details from an event in the last few months.  We'd love to add you to our newsletter list as we believe our articles would be of great value to you.  You can unsubscribe at any time.  If you don't want to go on the list in the first place, please reply telling us so and we won't bother you again.'

If you have collect cards from networking on an ongoing basis, it's a good idea to process them promptly.  Send a personal email 'Great to meet you last night.  Hope to see you at the next function. In the meantime I hope you don't mind that I've added you to our mailing list so we can keep in touch.'

There are laws depending on which country you are in that stipulates if double opt in is required or not. It is designed to stop people being loaded into an email marketing system without their approval. Some email marketing systems allow you to turn that off however, so best be sure you check the rules - if all else fails simply choose to 'double opt in' and you'll be safe.

It allows people who have subscribed to confirm they did indeed subscribe. This way, if someone else added their email address, they have the opportunity to ignore/unsubscribe or just rethink what they're doing.