No one who really knows is talking.
We do know that they rip open the envelope like a starving wolf as soon as they get it, take out the check, and cash it (assuming that you sent a check instead of paying by credit card online).
When they actually start processing your application, they send you a PIN for the web site (again, unless you signed up online).
The next step seems to be checking the application for completeness. At this point, if you forgot to sign something or didn't fill in some space, or your photo is unacceptable, they will notify you.
One set of prints goes to the FBI.
The other set of prints is checked against some state database.
They request a background check by DPS personnel in each county where you have lived or worked in the past five years. This seems to be the bottleneck, especially for Harris County.
Presumably someone checks for defaulted child support, state taxes, and student loans.
I don't know what they do with arrest records and dispositions. I suspect they just look at them to see if they meet some standard.
When all the boxes have been checked off, they print and mail your license.
All of the above is my understanding based on experience and several thousand reports posted to this forum.
- Jim
[Edited to correct typo]