Go to Apple menu -> About This Mac.
It should say either PowerPC or Intel, and a Mac OS X version.
PowerPC Macs can't use the most current version of iTunes, or sync with iOS 6 or later (which your new iPad Air most likely has on it).
Intel Macs can at minimum have Mac OS X 10.6 installed, a paid installer CD, and then a free 10.6.8 combo update to make them compatible with the latest iTunes. For more on getting to 10.6 and 10.6.8 see this tip:
https://discussions.apple.com/docs/DOC-2455
Do not update to 10.7 or later without reading this tip first:
https://discussions.apple.com/docs/DOC-6271