The Database of Intentions is a phrase coined by John Battelle in his excellent book The Search. Published in 2003, the idea formed the backbone of his book - the Database of Intentions is simply put: the aggregate results of every search ever entered, every result list ever tendered, and every path taken as a result. A pretty good market has been formed around the the expressions of customer intentions - the keyword.
The Database of Attentions is the aggregate user generated content at any one time across the entire range of social media. The real value of mining this database is dependent on marketers' ability to understand what the data is telling them and respond in a timely manner. Effective mining could and should also influence search strategies and therefore the competitive keyword market.
The partial view of the database above is from TwitScoop at 5PM on Sunday afternoon hence the heavy sport weighting.