If your site is setup with a payment gateway, your event registration, member dues and catalog sales processing will allow payment online. The credit card bypass option allows purchasers to skip the credit card payment form and choose to pay with a check or cash. This is the equivalent of a "Bill Me Later" or "Invoice me" option. The general setting for meetings is under Meetings > Settings > Payments, and is labeled "Allow users to pay by check or cash (credit card bypass)?"
You may also customize the message that appears. Additionally, there are other settings in General > Configuration related to bypassing payments. Search for BYPASS for a full list and descriptions.
Bypass Payment Location: Front-End
The bypass payment button is on the checkout screen during the final payment step.