If you're confused, that's understandable: OpenID is a little new, and will make more sense as an increasing number of sites on the web start to support it.
In a nutshell, OpenID lets you take your identity with you, proving to other sites on the web that you own a particular URL. LiveJournal's OpenID support lets you use your LiveJournal identity (just your URL) on other websites which take OpenID, and also lets you take your non-LiveJournal identity and use it here.
What does this mean?
-- leaving comments on other blog sites, and proving who you are
-- being able to add/trust/ban people as friends who don't have LiveJournal accounts
-- off-site LJ utilities that require you to prove your identity
It'll get more exciting as other sites start to support it. DeadJournal, since it uses the LiveJournal software, will likely be the first. As time goes on, there's rumors of upcoming support in Movable Type, WordPress, MediaWiki, Bugzilla, TypePad, TypeKey, b2, TextPattern, perl.org, and a bunch of other sites.
In a nutshell, whenever you see this little logo: , that means enter your LiveJournal URL if you want to prove to that site who you are. LiveJournal will ask you to confirm if you trust them, or you can say "trust that site forever". Never enter your password on a non-LiveJournal site. A site using OpenID doesn't need your password, and if they ask for it, they're trying to scam you.
That's it for now. More announcements as we continue to polish our OpenID support and more sites support it. DeadJournal should be this Friday, I hear.