I've been playing Arch for over four months now, and I still have no clue what credits are. I see people talking about them and offering to buy them all of the time, yet I still have no idea what they are. Can someone tell me what they are, what they do, how I get them, and how much they're worth?

Credits are basically $1 vouchers in the Arch store (so 1 credit = $1 USD). You have to buy them or receive them from other players. You can use them to redeem things in the Arch store :D

_pankake, I'm a greninja fan slide credits frfr

thx _pankake. how do I buy them?

Go to the balance in your profile tab. It will show ur balance(probably 0 if u haven’t alr bought). 
proceed to enter the amount of credits u wish to purchase, then choose a payment method(PayPal or stripe). Stripe is credit cards and debit cards so yea.