Deflation (falling prices or negative inflation) is sometimes confused with recession (or negative growth). The two sometimes go together, but not always - see "So this deflation... is it a good thing or a bad thing?" below.
WHAT HAVE OPTIONS GOT TO DO WITH IT?
An option is simply the right - but not the obligation - to buy (a 'call') or sell (a 'put') something.
They are more valuable the longer you have that right (because the market has longer to move in your favour) and the more volatile the market is - because the more the market swings about, the greater the potential gain.