To add a bit of detail...
From around the 700s AD, Wessex kings started to organise their territory into self-regulating districts called scirs - in modern English, �shires'. The shire around Southampton was one of the first. The actual main settlement, on the headland between the rivers Itchen and Test, was originally called Hamtun or Hantune, meaning �meadow farmstead'. If you put the three elements together, you get han + tun + scir. In the Domesday Book, created by the Norman invaders in the 11th/12th centuries, this was shortened to �Hantescire' and that is where the present abbreviated form �Hants' comes from.
(In the same way, the Old English Scrobbesbyrig mutated into Anglo-French Sloppesberie and the district - �Salopescire' - became shortened to �Salop' in reference to Shropshire.)