Your timestamps can own three different billing status:
2.) Do not bill
Billable timestamps (Bill) are calculated with an internal price, based on the user price (in the user settings) as well as an external price to the client (usually set in the project settings).
A not billable timestamp (Do not bill) is calculated internally with the price of the user, but is displayed with a price of 0.00 to the client and displayed in grey font.
A billed timestamp is marked green (Billed) and will not be added to any invoice anymore.
The total time is always calculated not depending on the billing status, because that's what the timestamp list is for.
When would you use "do not bill" timestamps?
Imagine you are working in the support department. A client calls and reports a bug. The time you are on the phone with him, must be documented, but you cannot bill the client for your time, as it's yours software fault. The bug can now be fixed, but the client must not be billed. Set the timestamp to "do not bill" and enter a comment to the timestamp, so the revenue department knows, why this timestamp is not billable.