Sanitas per aquam / Salus per aquas / Solus per aqua / Sana per agua / Solus par aqua...
Some folk etymologies are more common than others, but I have yet to see one half as fervently marketed as this one.
The word is not an acronym but an eponym, that is a name turned into a word. The name is Spa, site of the famous hot springs near Liège, Belgium. It has been used as a health resort since the middle ages and in particular during the 18th and 19th centuries. (The main attraction was often not the water but the opportunity to party with the rich and famous.) It got additional fame during World War I when the German HQ was located there.
Today Spa is possibly most well known (in Belgium at least) as a brand of mineral water, and (worldwide) for it's Formula One racing track, Circuit de Spa-Francorchamps. A particularly exciting part is called Eau Rouge Corner, "red water", which isn't a case of bad humour but an apt name for a stream that got it's name for it's iron-rich water.
The municipality of Spa (Spau, Spaw) is mentioned in English sources since 1565, and in the early 17th century the word was generalized to a common substantive meaning "health spring".
Arne Olofsson, professor in English
Repeat: It is definitively not an abbreviation for Sanitas Per Aquam, "health through water", or some other more or less grammatical and/or misspelt variation (one source suggested it was Greek). Neither is the name of the place an abbreviation. It is sometimes stated that the Romans wrote S P A on the walls of their baths, but there seems to be no records of such graffiti, nor anything resembling the term in their vocabulary. The Romans certainly indulged into bathing - the British Bath being a well-known example - but not in Spa.
The expressions salus/sanitas per aquam/aquas are grammatically and lexically acceptable for the sense "health through water" (salus and sanitas being synonymous and in nominative singular, aquam and aquas being direct objects in singular and plural, respectively).
The following list of "spacronyms" I've found - there are plenty more - begins with the acknowledged four. The others may be more or less correct, but none of them has anything to do with the etymology of spa. The sources are given as found.
Many sources claims the name Spa comes from Latin spargere, "pour" or "spill", which supposedly was a description of the hot springs. This etymology doesn't hold:
The verb spargere, which means "spread" rather than "pour", has no such form and an abbreviation to spa of any existing form would have been incomprehensible.
The place name is from Walloon espa "spring, fountain."