(Irssi2 name needs to be changed. Irssi2 has very little in common with irssi)
Shortly put, irssi2 is to instant messaging what IMAP is to mail. You can safely exit your irssi2 client, and irssi2 server just keeps on going. When you connect back with your client, you can see all the discussion that happened while you were away (and even older discussion, too, if you want).
You can also use multiple clients even at the same time, so you could for example keep one client always open at home and still be able to check what's going on with your mobile phone.
Irssi2 clients are encouraged to keep their configuration in server side, so nothing should prevent you from temporarily using another irssi2 client from your friend's home with no other configuration needed than irssi2 server's address, your username and password.
Irssi2 is designed to support multiple chat protocols (IRC, SILC, MSN, ICQ, etc.) but without ignoring hardcore IRC users. That means that unlike all other similar attempts (such as Jabber), irssi2's client-server protocol will actually allow fully featured irssi2 IRC client to be written with no compromises (but still the same client can be used to talk to MSN and elsewhere).
Note that irssi2 isn't trying to replace IRC servers (yet ;). irssi2 server simply connects to normal IRC servers just as a regular IRC client. To prevent mixups with these terms, IRC servers are usually called "gateways" in irssi2.