So I learned that the word dekansho is pretty big in Hyōgo. They have a Dekansho Matsuri and everything. My immediate question: What does it mean?

To summarize, it comes from a song called the デカンショ節 ("Dekansho-bushi" or "Dekansho song"). According to Wikipedia, it's a modern (as in Taishō) variant of an old Sasayama folk song called "Mitsu-bushi", that became popular with students around Japan after some a swimming club from what would later be absorbed into Tokyo University heard some students from Sasayama singing it in Chiba. (Got that?)

It gets better: the refrain dekansho is believed to have come from the philosophers Descartes, Kant, and Schopenhauer. The key lines in one version I have handy are:

デカンショ、デカンショで半年ゃくらす
あとの半年ゃ寝てくらす

Dekansho, dekansho de hantosha kurasu
Ato no hantosha nete kurasu

Spend half the year on dekansho, dekansho,
Spend the rest of the year sleeping

Of course there are plenty of folks (MIDI) who will argue that dekansho is a corrupted version of dekasegi shiyou ("Go out and earn some money [somewhere far from home]"), or that it's just gibberish that sounds good when sung in chorus by a bunch of dancing Hyōgoites, noting especially that it appears in rhythm-keeper phrases like "Yo-oi, yo-oi, dekkansho!" (and note that the more common rhythm-keeper dokkoisho is not far away)... but we don't have to listen to them. Descarte, Kant, and Schopenhauer it is.

Here's a rendition of 篠山節 ("Sasayama-bushi") that includes the variant line Dekansho dekansho de hantosha kurasu/ Nokoru hantosha nete kurasu. You can also see what is alleged to be actual footage of the dance in this video of NISHIDA Sachiko (西田佐知子) singing an entirely different song (that would be "アカシアの雨がやむとき", "When the acacia rain stops falling").