Only purchase a better quality amp if you plan on upgrading everything else later as well. A good amp will give you more volume as mrtycrafts stated, but will not do a single drop for sound quality. A good amp does what it is supposed to do- take input and output it exactly as it was input.
My humble opinion, if you have outgrown the sound quality of your current rig, opt in for some higher line L/R/C speakers as the next upgrade. That will give you a reasonable step up as the Yamaha has decent sound quality at it's price point. If that does not make you ultimately happy, then you'll have to upgrade to a better quality of processor/amplifier combo (or go with separates) and possibly your CD/DVD/BD player as well. That will give you a huge leap.
Once you upgrade something in the chain, more often than not you have to upgrade everything else to around the same quality level to realize the full benefit of upgrades. It is quite common to 'outgrow' and replace a complete system setup when you know that you are missing out on something sound wise. You can typically feel confident in 'going big' on quality speaker and separate amplifier purchases. These are items that rarely need to be changed and most future upgrades will be on processors (new features etc), and CD/DVD/DB players. Even if your current processor and players are not high quality, once you upgrade them down the road they still work fine with the quality speaker / amplifier investment.
I would venture to say the Polks are probably the weak link in the chain at this point, but this is just an underinformed assumption based only what you've listed for gear, and my experiences hearing those specific speakers- I don't know about the BIC subs as I have never heard them personally, but I can say I've always preferred a sealed sub to a ported/vented sub- I think the BICs are a ported/vented design?
Oh and welcome by the way, I saw that was your first post-
