The word spa derives from the name of the belgian town Spa (today best known from WW1, when the german high command resided there for most of the war) and means in a modern context usually a place or town where people go to receive medical treatments, generally involving some water, but in the context of the Garryowen song the word spa alone would mean the water from a mineral well, taken in a ressort town connected to said well.
The health benefits of the water from certain sources, be it by taking a bath in it, be it be drinking it, was already been known by the greeks and romans, the modern incarnation of the city of Aachen was founded by the Carolingians in the late 8th century due to the hot springs that exist there still today. Bath in England owes its name to such hot springs too. Other places, just like Spa, have springs the waters of which get drunk.
While such wells have been in use throughout history, places like this have e.g. in german usually a 'bad' (e.g. Bad Wildbad) in the name or a 'brunn(en)'/'bronn' (e.g. Heilbronn) , in french 'eaux' (e.g. Eaux-Bonnes) or 'baines' (e.g. Évian-les-Bains), he whole idea became fashionable for european nobility once Peter the Great spent some time in Spa in 1717 and really took off when Emperor Joseph II went there in 1781 to drink some 'spa' too.
From there on the hautevolee would meet in Spa for the summer, later in other places, Karlsbad (today czech town Karlovy Vary) and Baden-Baden come to mind. Dostojevskys novel 'The Gambler' for instance takes place for a big part in Wiesbaden.
http://whc.unesco.org/en/tentativelists/5934/
edit: typo