The blades act the same as your propeller. Each blade has 2 airspeed vectors: 1 resulting from the rotating blade itself (RPM on your prop), 1 from your aircraft moving in a forward direction. Combine these 2 vectors and you get the blade's resultant speed. If that resultant speed gets too low, your blade stalls just like any aerfoil. This is not dangerous in itself, it only causes performance degrade on your engine. A stall can begin to rotate to other blades, that is when a following blade of the same stage gets in the area of air where a previous blade stalled and thus also begins to stall. Thus your area of stall will move with the blades, but at a slightly lower speed of RPM, so each blade kinda moves through the area.
A surge is more dangerous. this happens when not only 1 blade stalls, but a whole set of blades in a disk (say e.g. a whole stage). If the next stage of compressor blades still works, the much higher pressure there will cause the air in the engine to be pushed back to the inlet, so you get a reversed flow within the engine itself. A surge is a cyclic movement of air going forward and aft within the engine. A surge is much likely caused by ingestion/damage and will cause more damage.
See the Thomson 757 birdstrike video
YouTube - ThomsonFly 757 bird strike & flames captured on video, the bird causes a whole stage of blades to go bananas and next you'll see a pulsating flame out of the exhaust, which is that cyclic movement of air of a surge.
During normal operation, jet engines use surge valves to bleed air and variabel guide vanes to guide the air and prevent surge.
hope this helps, a picture could be much more explaining