What is a BBTicket?
A BBTicket (BaseBand Ticket) is a secure signature that Apple uses to authenticate a particular baseband. An iPhone baseband is the cellular modem firmware that is on your iPhone.
BBTickets are similar to SHSH blobs which can be used to downgrade iOS firmware on A4 devices and possibly A5 devices in the future.
Why should I save my BBTicket?
You should save your BBTicket to increase the prospects of unlocking your iPhone in the future. Currently, there is not a tool to downgrade your baseband firmware, but that is likely to change. Even iPhone Dev Team member MuscleNerd recommends saving your BBTicket.
How to save your BBTicket
Step 1. Download TinyUmbrella 5.10.04 or later.
Step 2. Plug in your iPhone 4, 4S, 3GS or iPad 1, 2 or 3 (WIFi only models will not have a BBTicket.)
Step 3. Open TinyUmbrella and click on your device on the left under Connected Devices.
Step 4. Go to Advanced -> Check “Overwrite existing SHSH files on “Save SHSH.”
Step 5. Make sure “Request SHSH from Cydia” is UNCHECKED.
Step 6. Click “Save SHSH.”
Your BBTicket is now automatically included when saving your SHSH blobs using TinyUmbrella.
Update: Redsn0w has been updated to save BBTickets also. Download the latest version Redsn0w 0.9.10b8 here and read the comments in Update #3.