Triggers are used to define who is eligible for the offers.
For a primer on triggers and offers read this article.
This capability can be used to:
offer different pricing to retail and wholesale customers
offer different pricing to VIP customers
Customer = logged in
A customer, in the context of this article, means a visitor of your shop who has logged in to their account.
Edit the trigger that is associated with the offers you want to provide to customers. Navigate to the Targeting tab. Enable the Audience settings.
Set a filter
By default promotions are available to prospects (not logged in to your store) and customers (logged in, have an account).
You can configure if only guests, only customers or both are eligible. For the customers can additionally narrow it down to those tagged with a specific tag.
You can manually tag customers or use an app to automate the process. To tag a customer, open their account in the Shopify admin and set a tag.