Economic - they think they can run their own economy better than Westminster can
I think economically they may have a point.
I cannot claim expertise on the subject, but there have been articles in reasonably reputable magazines that made the case both for Scotland's great economy and predictions of a very rapid decline after declaring independence (e.g.
http://www.economist.com/news/britain/21606869-independent-scotland-would-be-rich-country-terrible-prospects-costly-solitude). Personally, I find the latter to be more convincing. But, just like you, I'm not Scottish, and I will probably be leaving the UK in about a year, so I can't say I care too much.
Political - an independent Scotland will never suffer under the yoke of a Conservative government
SNP have literally the same policies, except they don't understand how the current UK and EU governances work.
Cultural - Braveheart
Honestly, I think this is what it's all about. Decades of "ay'm Scottesh, not Britesh" mentality have finally compounded to the point where they think they need independence. I'd say that I'm confident they're in the minority, but I was horribly wrong about UKIP in European Elections, so I no longer trust my guesstimates of political popularity.