Here's the basic idea of blind signing in Chaumian e-cash:
Let's suppose that a central issuer (Chaumian e-cash is centralised) has an account in my name with a value of 10 dollars. In order to "withdraw" this money as 1-dollar "bills" I begin by generating ten random serial numbers, each long enough that I can be reasonably sure no one else will generate the same numbers.
I am going to have the central issuer sign a message saying these are now worth one dollar each, only I don't want the issuer to know which bill is which (otherwise they could just match up outgoing and incoming serial numbers to know who I spent it with, since Chaumian e-cash can only be spent once before it has to be re-issued).
So in addition to the serial numbers I also choose secret 'blinding factors' and combine them with my serial numbers. I give these blinded serial numbers to the central issuer, and they sign each one with their 1-dollar key (they have different keys for different denominations) and reduce the amount in my account with them accordingly. They know how many 1-dollar bills they signed, but they don't know what serial numbers were on each bill they signed.
Now, the trick with "blind signing" comes in. Because of how blind signing works, I can now remove the blinding factor, but I still have a valid signed message which can be verified using the issuer's public key. This gives me a signed one dollar bill with its own serial number that the bank doesn't know (but they do know how many one dollar bills they have signed, because each one can only be un-blinded to a single serial number).
Now, to spend the bills to someone else, I simply show them the un-blinded, signed serial number. They must now immediately "cash in" this token by going to the central issuer and showing them the signed serial number. The central issuer verifies the signature using their "1 dollar" key, records the serial number, and credits the new person's account. From their perspective, this dollar is indistinguishable from any other they have issued in the past.
However, if someone else shows up and tries to cash in the same dollar again, they will not honour it because they have already recorded the serial number as spent. You also cannot spend a $1 serial number as a $50 serial number because $50 serial numbers use a different key.
More details about e-cash, including an "offline mode" that relies on trusted hardware, can be found here. They use a different method of ensuring a $1 bill is not spent as a $50 bill--I don't remember which variant is whose but there are several of them which basically accomplish the same thing in slightly different ways.