In the early days of fan engines, compressor stalls were a regular occurence. As far as i know, it is just caused by sticky or failed pressure relief valves in the engine- when the overpressure builds up in a section, it can 'cough' loudly. At night it is spectacular- you get instantaneous flames and 20' sparks coming out of the engine, accompanied by a canon shot sound. You can imagine the effect in the rear galley of a VC10 when the engine 5' away surged! It used to burst the knicker elastic of the girls working there! The 747-100 was a merry surger. As long as the parameters recover, you didn't have to shut down. Indeed, for a long period, it was permissable to try a re-start even if you had to shut down. Most surges happened when you made significant power changes, and the vast majority at altitude. Low altitude surges were virtually unknown.
They are not a structural problem with an engine and appear to cause no undue stress- just alarm. The CFM-56 seems to be a most stable and reliable engine, and I have never known it to surge, or even heard of it happening to others. I was once sitting next to B707-336 No. 3 engine at night when all hydraulics were lost in the flare. The only way to stop was holding full reverse on until stationary. It was repeatedly surging right next to me, banging and flashing and flaming. I really enjoyed the 'firework show'- it was excellent entertainment! Then they had to pull reverse on to stop rolling and hold it and it was surging away again. All quite harmless, but very noisy.
All that old fun has ended now- I never had a surge on a 747-400 in 8 years. People can't believe how harmless they can be, which is why the 747-400 ex LAX-LHR 'incident' raised so much concern about damage to the airframe- there was nothing wrong with it at all, just a sticky valve in the engine.