"Big data is a term used to refer to the study and applications of data sets that are too complex for traditional ... software to adequately deal with" (Wikipedia). It's "an evolving term that describes any voluminous amount of structured, semistructured, and unstructured data that has the potential to be mined for information" (TechTarget) but that "is difficult to process using traditional database and software techniques" (Webopedia). Some people say that "big data is not a function of the size of a data set but its complexity. Consequently, it is the high degree of permutations and interactions within a data set that defines big data" (Technology Review).
A definitive guide to data definitions and trends, from the team at Stitch.