Before that Broadcom was (and still is) one of the larger communication hardware companies, making chips for cell, wifi, bluetooth, ethernet and ARM SoCs, along with telecom and data center boxes that used these chips. You almost certainly have their hardware in some device you own. But they have always had difficulty competing with Qualcomm, arguably in part due to anticompetitive behavior from the later.
After the acquisition, they have been acquiring enterprise software companies to diversify, including CA Technologies (think Atlassian/Oracle of the mainframe world), Symantec, and now VMWare.
Given that CA already had the reputation of "where software goes to die", this is ... bad news for VMWare. (I'd heard that description from many in the tech field, including from a CEO who's previous venture had been acquired by CA.)
I also hadn't realised that Broadcom itself had originated at HP.
Its history goes back to the 1960's. It is a major semiconductor company that I would say, was part of the ecosystem that made computers and networks possible.
You haven't heard of them because they make too much of everything that makes the fabric of everyday computing.
It's like how you would never really know of the company who made the pipes for your toilet/plumbing.
