These cases work in the same way as all other bPay devices -- and contactless cards, for that matter. Tap them on a contactless reader to make purchases of up to £30, with those funds coming from a mobile wallet you can top up with any UK-registered debit or credit card with Visa or MasterCard stamped on it. You monitor this virtual piggybank online or via the companion mobile app, and you can set it to top-up automatically when the balance is running low.
While that's all well and good, these cases are easily the most pointless addition to the bPay range. As long as you have a relatively up-to-date smartphone, you already have access to bank-agnostic mobile payments through Apple Pay and Android Pay. These are also better options, since active authentication means purchases aren't limited by the £30 cap.
Barclays is well known for being cold on these third-party payment platforms, of course. Earlier this year, the bank became the last big institution to support Apple Pay, nine months after it launched in the UK. A similar situation is happening with Android Pay, which came to the UK in May. There's a chance Barclays may hold out on that front forever, though, since it already has its own app for that.