edit: I typed this on my phone while waiting at the airport, so it's a little looser grammatically than I'd like.
I've been out of the network management space for about a decade, but ostensibly the big screen was pitched as a way to look at overall network health or identify a large-scale outage. There'd be a big-ass network topology map that would suddenly start showing red dots.
For the big topology map, that was usually done using Spectrum or Openview Network Node Manager (the only use we had for NNM for that matter, it sucked at everything else).
The reason I said "ostensibly" though, is because if you're relying on noticing red dots appear on the map to tell there's an outage, it means you aren't doing proper event correlation.
Most systems we built focused on the event viewer (Netcool for the most part, but it was just for deduplication as it didn't do actual correlation); so that's what would generally be on screen for an analyst. Their other screen would have their ticketing system (usually Remedy, but occasionally Vantive, which I vastly preferred).
The actual correlation engine was Nervecenter for the most part (which was a consultants dream as it took like 6 months to build all the rules), although we tried out a bunch of the "code book"-based correlation engines (SMARTS I believe was the name of one of the more egregious ones).
I worked on one project to build a NOC for Raytheon that 6 months into it they decided to make the whole thing automated (as in, not have any analysts actually working in the NOC) and that was interesting. We ended up having to write logic to handle all the notifications and queuing.
Like I said though, all of this was the Cretacious period for network management, so I really hope things have gotten better in the interim.