A Field HQ is a 5 TP building. It is very fragile and offers no protection, even with the sandbags out in front of it. It has one trait: every wave, it has a 25% chance of giving you one extra TP. When you have earned a total of 1000 bonus TP, you will get a cool medal, increasing the chances by a further 5%.
Try not to get too greedy: if the HQ is blown up, you lose all the TP you have gained from it. For example, your Field HQ has produced 30 TP. It gets blown up, and you had 5 TP. Since the TP produced will get deducted, you would end up with -25 TP.
However, if built early on, the Field HQ can provide extra TP to build up your early defenses.
If you decide that a Field HQ is worth the risks, make sure to have it protected!
Field HQ's are known to stop functioning after wave 100, so if bought at the very start of the game, they should net an average of 25 TP the entire game (without the ribbon).
Note that you can also get a Mobile HQ, which is a Half Track with a Field HQ in it along with a radar and an antenna. A good idea is to put it in a pillbox so it's nearly impossible to destroy.
Field HQ's do not give you TP in last stand.