Usually "Big Four" refers to the 4 largest accounting firms: Deloitte, EY, KPMG, PWC.[1] If it's referring to tech, that's an odd/confusing usage when "FANG" is so prevalent for the same concept but explicitly for tech.

[1] https://en.wikipedia.org/wiki/Big_Four_accounting_firms

In my experience, the vast majority of people in tech are completely unaware of the accounting usage. I only know it because my two siblings work for two of them.

Usually some subset of Facebook, Amazon, Apple, Microsoft, and Google

So Big 5, really, but I feel Apple is usually omitted because its primary focus is consumer hardware and the software is usually an ancillary product.