Whenever you want to write to your customers for marketing purposes, you need their express consent.
For example, the typical check mark that you set when placing an online order or filling out a contact form and thereby expressly agree to be contacted for advertising purposes.
This is called an opt-in. A double opt-in is when you have this consent confirmed again. For example, by sending an email with a corresponding link that the user has to click on again.
More details in the blog: Double opt-in with Mautic