Big data is code for difficult data. More precisely, it is any data set where traditional techniques (databases and software) are inadequate -- whether trying to to store, query, manipulate, analyze, or otherwise use the data.
Because (by definition) Big Data is difficult, an industry is springing up, with various database, software products and analytical techniques to address the most common problems with traditional techniques. These are often described using the three (3) V's: Volume, Variety, and Velocity. Essentially, data sets that become too big, contain incongruous data types (such as video files, images, documents, and text and numerical values) and require real time storage (such as click behavior online or sensor outputs from satellites, cell phones, and vehicles).
The Big Data industry as a whole, in an effort to solve the 3Vs is still evolving as to how it will provide additional, non-obvious meaning difficult data giving rise to Data Science and Big Data Analytics.