The AH Count in the Nitelog program shows the Apnea-Hypopnea count.   This is the total amount of obstructions during a certain amount of sleep.  Apnea means periods of no breathing and hypopnea means abnormally slow or shallow breathing.

The AHI, or Apnea-Hypopnea Index measures the apnea severity.  When you see the AHI it is the sum of the number of apneas plus the number of hypopneas that occur, on average, per hour.