From the Twitter Blog:
Yesterday, we updated our Android, iOS and mobile web apps to make it easier for you to find relevant content when you’re on the go. We also started to roll out an additional update on our mobile apps as well as on twitter.com: you’ll now be able to find older Tweets using search.
Previously, Twitter search results displayed Tweets going back about a week. We’ve developed a way to include older Tweets, so you can see content that goes beyond the more recent Tweets.
As we roll this out over the coming days, the Tweets that you’ll see in search results represent a fairly small percentage of total Tweets ever sent. We look at a variety of types of engagement, like favorites, retweets and clicks, to determine which Tweets to show. We’ll be steadily increasing this percentage over time, and ultimately, aim to surface the best content for your query.
See Also: More Info, Discussion, Screenshots on Search Engine Land
We agree with Danny Sullivan that use of Twitter’s advanced search interface as well as Topsy, a third-party Twitter and social media search tool (alerts too!) can be very useful when in search of older tweets.
See Also: All of Twitter’s Advanced Search Operators Work From Any Twitter or Topsy Search Box
Note the since: and until: operators.