Simple explanation
here
In a turbine engine, compression is accomplished aerodynamically as the air passes through the stages of the compressor, rather than by confinement, as is the case in a piston engine. The air flowing over the compressor airfoils can stall just as the air over the wing of an airplane can. When this airfoil stall occurs, the passage of air through the compressor becomes unstable and the compressor can no longer compress the incoming air. The high-pressure air behind the stall further back in the engine escapes forward through the compressor and out the inlet.
This escape is sudden, rapid and often quite audible as a loud bang similar to an explosion. Engine surge can be accompanied by visible flames forward out the inlet and rearward out the tailpipe. Instruments may show high EGT and EPR or rotor speed changes, but, in many stalls, the event is over so quickly that the instruments do not have time to respond.
Once the air from within the engine escapes, the reason (reasons) for the instability may self-correct and the compression process may re-establish itself. A single surge and recovery will occur quite rapidly, usually within fractions of a second. Depending on the reason for the cause of the compressor instability, an engine might experience:
1) A single self-recovering surge
2) Multiple surges prior to self-recovery
3) Multiple surges requiring pilot action in order to recover
4) A non-recoverable surge.
or a bit more complicated
here.