twister is a microblogging peer-to-peer platform, that is, it is a distributed system like bittorrent or similar file sharing technologies. Being completely decentralized means that no one is able to shut it down, as there is no single point to attack. The system is also designed so it cannot be censored, freedom of speech cannot be taken from you. And because the cryptography is employed end-to-end, no entity is able to spy on your communications.
I think that the Peercoin community should be on twister 8)