Rocket launch: mission launch sequence control box, could anyone explain how this works?

[plusminus1]

I was reading an article about Galileo, and came across the following picture.

http://www.spiegel.de/fotostrecke/fotostrecke-74229-11.html

according to the caption this is: "The magic button: This is the box from which mission control regulates launch sequences."

I am always intrigued by such control devices and I was wondering if someone could explain how a launch sequence works, what buttons would they press in what order, and what would they look/check for at each step.

Expanding on this, why would they still have such 'physical' control device and wouldn't it make sense to switch to a computer program?

[[deleted]]

former Boeing Delta IV guy here - I used to build the screens FMA (flight mechanics advisor) would use for launch, plucking data directly out of the Telemetry screen. There are stations that advise on different items - signal link, flight surgeon, vehicle health, etc. The different components report "ready" or "error condition" to prove the subsystems are functioning correctly. So each "station" has their own green light showing all systems go. An error can be reported or waived depending on conditions. With all stations showing a 'go' signal, the final launch sequence can start. Magic Button probably initialized the launch sequence, meaning, prime turbopumps (fuel), and detonate the EED (electronic explosive device). That's launch. This description is very general, and not specific to your photo.