As the website states, it's not a new cryptocurrency coin. It works only if the bank wants to support it since GNU Taler is more like a plugin. When you want to pay a merchant, it directly withdraws money from your bank account and converts it to coins for your wallet to deposit. The bank knows where this coin is sent. However after depositing, the wallet tries to pay the shop. At this point, afaik the wallet makes a cryptographic proof with details like the amount of coins, sends it to the bank and the bank blindly signs it with their private key. Blind signatures are signatures where the signer does not know what the contents of what they are signing are. So the other bank or the shop can know that it came from that bank without the bank knowing from where the coins came. The bank however knows where the coins are going, so you can hold them accountable in case something happens. But you of course must reveal your identity for those things. Since cryptography is used, you can prove payments to merchants. GNU Taler can also be used offline, but I don't know how that works.

(there might be misconceptions in here so don't take my words blindly)

Here's a nice image I found online: