It has been reported to media outlets such as The Next Web that some users are seeing the ability to download their entire archive of tweets.
As said in the title, this is only for a limited amount of users. Twitter's CEO did say earlier this year that users would be able to download all of their tweets by the end of this year. It's getting near the end but it seems that Twitter will pull though.
When you download the tweets, you also get the CSV and JSON files, completing the meta data. You also get HTML as well, so it's like having a twitter webpage but offline.
If you were chosen as one of those to have this feature early, then the feature is at the bottom of your settings page. If not, then sit tight. Expect a more wider roll out soon enough.
If you were one of the lucky ones, let us know in the comments below.