As Firbird correctly states 'A hung start is when fuel is applied and exhaust temp is noted but the engine will not accelerate.'
But a bit deeper - it is usually when full ignition of the fuel in the combustion chamber does not take place, normally attributed to an inop ignitor or HEIU (there are two per engine). As all the fuel is not ignited the turbines are slower to rotate which in order is slow to rotate the compressors (HP & (IP) & LP). This manifests its self as low pick up on the N1 and N2 indications in the flight deck. The engine will take longer than normal to reach self sustaining speed - if too long the engine may self abort the start but hopefully the operator will notice it and terminate the start. The starter valve will only rotate the HPC to a nominal percent (usually 40-45%) and this is usually the RPM at which the engine 'hangs' Allowing the hung start to go its distance is bad practice as once unburnt fuel is ignited it can torch back to the NGVs/ HPT causing damage.
A hung start can also be attributed to late opening of the throttle control valve which would be shown as no initial ignition followed by a sharp rise in EGT/JPT/TET.