Anyone know anything about how broadband actually works?

A cable router, so no use to anyone on ADSL, and if Virgin are giving them away free, won't all their customers have them anyway ?

to my knowledge, Virgin routers only work with virgin cable modems, they have their own proprietary firmwares which you cannot change. So probably worthless to most people.

Not exactly. Virgin give you a cable whatsit that plugs into the cable connection and then you use Cat5 to plug a Netgear wireless router they also supply into that.
Perhaps on the cheaper (non-wireless) plans you don't get a router but on the wireless ones you definitely do.