Discover: Thursday's update brings the Discover tab from Twitter on the web to its mobile app. Much like the web version, the Discover tab lets you know what tweets people you follow have favorited or retweeted. The tab also lets you know if someone you follow has decided to follow a new person or add a new person to a list.
Activity appears below stories in Discover, and tapping on a story will let you see more tweets about a trend or news story that can be replied to, retweeted, or favorited.
Search: The updated apps have improved search functionality, which offers suggested spellings and related terms when you search. When performing a search for people, the app will autocomplete searches for people you follow when you start typing in his or her first or last name or username.
Specifically for the iPhone, Twitter has added the ability to tap the search box in Discover and see your recent queries, as well as the ability to go directly to someone's profile when searching for a username in Connect.
Notifications: Twitter's app now supports push notifications for interactions. Now you can choose to be notified when someone new follows you on the service, or when your tweets have been retweeted or favorited