Publishing the website allows you to open your website so customers would be able to place orders through it.
Unpublishing the store would show:
Sorry!
We can't receive your order at the moment
Note: If you want to stop receiving orders for a while, it's better not to unpublish your store. Instead, set the store to Busy mode — this keeps your website online but stops new orders during the time you’ve set. Check this article on How to set the store as busy.
To publish or unpublish your website, follow the steps below:
1- Click on the store name on the top left of the Dashboard
2- Click on [Publish] to publish the website or [Unpublish] to close the website
To watch a video of all the needed steps to publish/unpublish your store