Customer Assist allows you to log into the Webstore as a customer. Customer Assist works best when you are already logged into the Webstore with an account that has administrative privileges. Then, pressing Customer Assist from the customer service screen launches you right into the customer's account. You will know you are customer assist mode based on the Blue bar at the top of your Web browser.
The customer will not be able to see your session; this is not a shared session, you are simply logging in as them to either view something on their account or make a change to something on their behalf.