The language the Twitter user selected from the drop-down list on their Settings page.
It is an indication of their primary language but it might be misleading. For example, a user might select French as their mother tongue but compose their Tweets in English. DataSift offers an augmentation called Language which determines the language based on a statistical analysis of groups of characters.
The drop-down list shows the full name of the language (English, French, German, and so on) but the twitter.user.lang target contains the code for the language.
Take a look at the list of languages that Twitter supports.
Filter for Tweets from authors who specify French as their preferred language:
twitter.user.lang == "fr"
Filter for Tweets from authors who specify French as their preferred language but Tweet in English:
twitter.user.lang == "fr" and language.tag == "en"
Filter for Tweetz written in Lolcat:
twitter.user.lang == "lolc"
You might need to wait for these to show up. At the time of writing there are fewer than 100 per hour but if you're patient you'll see them.
Target service: Twitter
Target object: Twitter: User
Always exists: No