We have these things called stream ciphers. You put a little bit of randomness in, and you get what seems to be lots of randomness out. For example the cipher might need a 256-bit key and 128-bit nonce and then spit out gigabytes of seemingly random data.
Now, mathematically they can't /really/ be making more randomness, there's no random steps it's all deterministic, in principle it ought to be possible to unwind the steps and get back the initial random state. But it turns out that unwinding step just can't actually be done with a good stream cipher, that's the whole point.
We do this sort of stuff a lot in real modern cryptography. There's a HN article which might still be on the front page, it was earlier today, explaining how SSH works. It shows that six keys are needed for SSH encryption, but they don't go get six times the randomness you'd need for a single key, they can just use a cryptographically strong hash function and make six different keys from the same shared secret randomness.
Let's do an experiment:
I've rolled my hex dice a few times to create a 64-bit random number.
I've pushed that as ASCII text into MD5 and got back a result, and now I'm going to tell you the first and last characters of the result:
F31FB042................81AFD8FA
That's 64-bits. If you were correct with this idea about entropy you could tell me what the missing bits are, infact you could prove it to other posters - after all I have given you all the randomness according to your thinking, there can't be any left.
But in fact you have no idea what those missing bits are, no idea what the original 64-bit number was, because you are wrong, with cryptographic primitives like hashes or stream ciphers we can in practice take a relatively small amount of entropy (like a few minutes of keyboard bashing by a toddler) and that's enough for all purposes.
The _real_ reason you shouldn't use this to make passwords is that the site might be lying and keeping a record of every password that is chosen and which IP address it was given to etcetera.