In spite of its relative young age, Thunderbird is a mature application, so you should not come across a crash too often.
The first two screens of the Mozilla Quality Feedback Agent will introduce you to the Agent, and its privacy policy (no emails are being sent, only data necessary to troubleshoot the crash). You can click Next (recommended, don't you want to improve Thunderbird?) or Cancel.
the last step gives you the option to uncheck the Turn Agent on checkbox. Here again, we recommend leaving it checked, so that your crash will contribute to bettering future releases of Thunderbird.
In the next screen, the Agent gives you the option to enter your email address, signup for Mozilla-related information updates, and describe what happened, and possibly directly send incident information in the future.
From this screen, you can also click the Show Details button, which will reveal details meaningless for mere mortals: a description of Thunderbird's state at the time of the crash.
If only for the fun of it, you can save you crash data information as a text file, after which you can allow the Agent to report your crash data to the Mozilla developer team, and claim your fair share of contribution to the next release of Thunderbird.
If you are running Windows XP (Home or Pro), chances are that the Windows crash utility will popup too. This behavior is normal, and simply part of a similar process to ameliorate Windows by reporting crash data.
As for the Mozilla Quality Feedback Agent, we recommend that you do let the Windows crash utility report the problem to Microsoft, (even if the problem may have been more relevant for Thunderbird than Windows developers).
After all the crash reporting is done, restart Thunderbird, and ensure that all your emails are still there, etc. This would be a good time to have a look at our Thunderbird maintenance tutorial.