Can't say for sure, but if it's anything like a background check done for a security clearance, it probably involves speaking with current and former employers, neighbors, friends and acquaintances, school classmates, teachers, etc. Chances are pretty good they won't dig too deep because it costs a lot and takes a lot of time.
I would venture to guess it's probably checking city,county computers for warrants and then running a CCH(computerized criminal history) for past arrests. All of that takes 2-3 minutes tops especially if the person has no arrest history.
here in nc they have that part go to the local office of behavior(?) to check if ya been institutionalized, or have a mental rap sheet, as i understand it, and that they do not have a report of any domestic violence records on you.
Not being familiar with Texas law, I can only proffer a guess. When I conducted a "field" background investigation on a police applicant, it meant I would go into "the field" and check with neighbors, referrals, employers, co-workers, the whole enchilada. You can learn a lot about someone by making personal contact, as opposed to a form letter. Ex-spouses can be particularly informative.
Because they are very expensive and labor intensive, I doubt the local cops have a budget that would allow such an investigation as a matter of routine for a carry permit. I can also hazard a guess that if you check "no" on the application, the background check is immediately over, as in "What does this guy have to hide?" Maybe they just want to see how you answer the question.
if you want to get awareness, you need to background check the companies or person what you looking for. It's also better to choose the accurate background checking. So you'll not waste time and money.
It took me 3 months to get my permit here in Texas.
Part of the field background check is the state does a check of any and all taxes, alimony, child support, etc. on you. If the records indicate you owe anything regarding any state or federal money, you have to send proof it was paid.
The state law says the license shall be issued 60 days after the state recognizes your application (they send you a dated letter). Be prepared to wait.