Your intuition is correct. Big data refers to extremely large data sets, often with millions of data points growing from people's behavior and interactions. Businesses analyze big data to improve future products and make better business decisions.

Your intuition is partially correct. Big data refers less to the volume of individual data points and more to the size of each of those data points. A data set may contain only a few values, but if each of those values has, for example, more than $99$ digits or $100,000$ characters, they constitute big data.

The truth is$,$ big data is a widely misused term. Yes, it does refer to extremely large data sets, but those sets are exclusively academic in nature. In business contexts, the proper term for data sets of comparable size is "high$-$scalability data."