Although I believe "big" usually refers to the size of the dataset, I originally heard the term used in the same sense as "Big Oil" - and the implication was that as companies collected massive amounts of data and figured out how to profit from it, "data" was going to become the next high-value commodity.
edit: Although to answer your actual question, it's a bit like "cloud computing" - it probably refers to very scalable systems with an emphasis on reading, writing, and processing large amounts of data - but really it's a bit of a marketing term :)
To branch off of your comment, which is the best description of it, I think it should be noted that for the past two years this subject has been the most nominated topic across all of our events for both information and security officers (the company I work for empowers F1000 C-suite executives to come up with relevant material for their peers to discuss annually). For companies that are inundated with web analytics, feedback they're getting from and trends they're seeing on social media to sales numbers and any other quantifiable data, they're trying to tie it all together so they can make changes or create new opportunities for their markets.
edit: Although to answer your actual question, it's a bit like "cloud computing" - it probably refers to very scalable systems with an emphasis on reading, writing, and processing large amounts of data - but really it's a bit of a marketing term :)