A cut-off time is the time at which you stop processing orders for the current day. If you have your courier pick-up parcels from your warehouse at 19:00 then you would set the cut-off time to 19:00.
E.g: Lets say you offer next day delivery and have a cut-off time of 19:00 set. If a customer orders at 17:00 on Monday then they will be offered delivery options from Tuesday onwards.
If they order at 19:30 on Monday they will be offered delivery options from Wednesday onwards.
This configuration option can be found under
System>Configuration>Shipping Settings>WebShopApps Date Based Shipping