It is enormously handy to be able to "record" a single event and then look at it in your leisure. To zoom in, and inspect one part of the event, etc.
Imagine something like testing a button bounce (or relay contact bounce). You hook up the scope, press the button, and it records the button bounce and displays it on the screen. Then you can zoom in, see how many times it bounced, what the timing was, how well your debounce circuit fixed it etc.
Or it can record the waveform an oscillator makes at the moment it powers up. You can record it and see it ramp up to full freq/amplitude etc over X mS. See how long it takes to stabilise.
With a normal scope you can only view the oscillator waveform once it is running.
