Internet outage from broadcast traffic

Today our enterprise internet provider reported their major outage incident (all their Sydney services it appeared) was due to “a large amount of broadcast traffic received by a border router”. As usual, we approach these incidents with a series of follow-up questions about risk management to the vendor. Is anyone able to succinctly explain how, conceptually, broadcast traffic would be received by a [border] router and then why that would cause intermittent and extended outages? Essentially: how does broadcast traffic bring down a router?