Compressor stall and surge:

‘Surge' can occur in both centrifugal and axial flow compressors and is the reversal of the airflow in the compressor. It is a very undesirable condition, which can rapidly cause serious damage to the engine.

In an axial flow compressor, ‘surge' is nearly always preceded by stalling of some of the compressor blades. An aerofoil is said to be in a stalled condition when the airflow over its surface has broken down and no lift is being produced. If a row of compressor blades stall, then they will not be able to pass the airflow rearwards to the next stage and the airflow to the combustion chamber will ultimately stop.
The lack of rearward airflow will allow the air in the combustion chamber to flow forward into the compressor until it reaches the row of stalled blades. Then a violent backwards and forwards oscillation of the airflow is likely to occur, which can rapidly cause extensive damage to the compressor blades and also over-heating of the combustion and turbine assemblies.

Stalling of the compressor blades can occur for various reasons and to appreciate how the condition comes about, a review of aerofoil theory and its application to the compressor is required.