What's the purpose of running Armory through Tor?
Armory (in online mode) uses a full node.  Full nodes relay transactions for other programs on the Bitcoin network, so by running Armory on Tor, you help other people send their transactions with possibly-improved privacy.
Sending your own transactions through Tor with Armory can help prevent anyone from associating your IP address with your transaction, possibly improving your privacy.


Note: Tor and Armory must both be used properly to achieve improved privacy.