The system does not ensure anonymity as to who has voted, but it does maintain secrecy as to how you voted.

The idea is that you can have a public, verifiable "ledger" of voters. You can verify that you are on the list with your encrypted vote. I.e. you verify that your vote counts. You can match it to the receipt you received when voting. You do not, however possess the key to decrypt your vote or the vote of anyone else.

The public list can also be used (more work) to verify that only real people voted: They could presumably be contacted.

Homomorphic encryption allows the votes to be tallied while still encrypted. The result is an encrypted tally.

At this point someone with the decryption key can decrypt the final tally and reveal the result. Presumably this can happen per polling place.