Twitter's own app has always been a bit behind the curve as there are a number of third-party apps that outshine the official app. The service's newest update, though, seems to have made the app relevant again.
Most users, I think, will be happy to find that users now receive push notifications from the application. This way, you can receive Twitter updates even if you're not in the app. This is much better than it was previously, since pulling data does seems to drain the battery much more quickly.
Users can also hardwire what kind of messages they want to receive. Just tap-in to your settings, and select whether you'd like to be informed when you receive direct messages, mentions or just tweets from your followers.
As a person who has multiple Twitter accounts, I was especially pleased to learn that Twitter now allows users to remain logged-in with multiple accounts simultaneously. In my opinion, this is where Twitter was always light years behind apps like TweetDeck, Plume and Seesmic because it was frustrating to have to log-out and sign back in each time you wanted to tweet under a different Twitter user name. This is what made me stop using Twitter and switch to a third-party app altogether.
The app never really ran poorly, but the developers have tightened the screws and made a few bug fixes. Tweets seem to load more quickly, and the app has less difficulty jumping between tabs than before.
The home screen widget also received a slight makeover. Overall, it looks a little more polished than it did before, and the format is similar to the kind of setup you see at TweetDeck. Not to discount the improvements, but TweetDeck still seems to be the classier, more sophisticated-looking app.
It's nice to see that some of these other clients are clearly pushing Twitter to improve their application. I take that to mean that these applications will continue to improve with time.