Trooper badges, currently awarded at 25 per trooper used or time your champion gets used, are one of the game's many currencies. While it's not one of the currencies new players typically obsess over, experienced players expect to receive badges from every trooper on their list daily or they're inclined to drop that player, and it's all because of the badges.
If you open the trooper store, you'll see what you can buy with the badges. But what's often overlooked is that you can't actually earn enough to buy EVERYTHING in the store each month.
Collecting the badges should give you a continual weekly stream of souls, fragments and skill shards. However, they're also a good source of powerful talismans. Check out the store weekly (it resets weekly on Sunday GMT, which means some time Saturday for those of us in the US) and see what you can grab to improve your team for those badges.
If you were to get every badge possible, that would amount to 25 per x (50 troopers + 50 troopers using your champion) = 2500 badges. This amounts to 17,500 per week, and at least 70,000 badges monthly. That should get you most everything you would like from the store.