datasets large enough that it was impractical to try to store or work with them in a traditional relational database software

How I remember it is that it’s not even the whole dataset that is too large, but the individual records. Hadoop for example is not doing anything magic, it’s just a software package to extend MySQL to be able to efficiently have pictures (Facebook’s original use case, of course it evolved) as records.

I guess big data is what you need it to justify what you want to justify. In one of my gigs’ case, it was public funding for a project.