Mountain Lion adds direct Twitter support in the OS, just as iOS users have had for a while. If you haven't set up your Twitter account yet, you'll want to go into System Preferences, and then choose Mail, Contacts & Calendars to set up your various accounts.
Just like on the iPhone and the iPad, you can now set up certain cloud services in OS X. Your iCloud and mail accounts are in there (for Microsoft Exchange, Gmail, Yahoo!, and AOL), but there's also now logins for Twitter, Vimeo and Flickr as well.
Logging into those is as easy as logging into the main sites, and especially if you share information and links often on social networks, it could make things a lot easier for you.
The one big drawback is that Facebook integration is not yet included in the OS. It was tested during the beta, but it won't be available to the public until a software update this fall. Until then, you can still log in and set up your other various accounts. Also, as has been pointed out on Twitter itself, the Mountain Lion tweeting option via the Share button opens the Twitter website only -- it doesn't (yet) work with native clients like TweetDeck, Twitter for Mac or YoruFukurou.