1. How the Save option works
Your customers can save their designs by using the "Save Design" button.
The designs get saved in the cache (and they will be available to the users as long as they do not clear the cache and stay on the same device from which they saved the design) unless your customer is logged into your website. In the latter case, the designs are permanently saved in the Zakeke back-office and your customers find them in the customizer under "My saved designs" and you can access them from the Customer saved designs section in the back-office.
IMPORTANT: even if the customer is logged to your website, designs won't be saved in his/her account on your website and he/she still needs to access the customizer to find the saved designs.
2. Managing the option
The Save button is enabled by default. If you wish to disable it for your products, you do it via Settings > Interface Editor > Actions and uncheck the option "Enable "Save design" button"
3. Customer saved designs
Designs are saved by customer ID or email, depending on the e-commerce platform. Also, you can search them by tags.
Saved designs can be edited by you by clicking on the edit button (pencil symbol). Once you've edited a design, your customer will find the edited design in his/her gallery in the customizer ("My saved designs").