H = Healey
A = Engine displacement between 800cc and 1999cc (originally meant between 800 and 999cc, but since "B" meant an engine between 2000 and 2999cc and there was therefore no letter between A and B to designate an engine between 999 and 1999cc, A came to mean "below 2000cc").
N = 2-Seat Tourer
8 = 8th model in the series (nobody seems to know why the Sprite "series" started with 5).
L = Left Hand Drive.
5560 = The individual chassis number.
HAN8L5560 is a Mark III Sprite with a 1098cc engine, at least originally.