Available miles are the total sum of miles you have available to purchase award tickets, use for flight upgrades, etc. Available miles are miles that are redeemable for things.

Qualifying miles are not really "miles" per se, but they are a sort of counter that keeps track of where you are on the way to earning elite status. For example, Silver elite status starts at 25,000 Elite Qualifying Miles (EQMs for short).

Your "available miles" and "qualifying miles" may never actually be in-sync. If you have a WorldPerks Visa card for instance, you'll earn WorldPerks miles for your purchases and they will add to the total of your available/redeemable miles, but they'll never affect your qualifying miles (unless there's a promotion). Or, you could buy a higher fare class that rewards you with extra qualifying miles but you still earn the same number of redeemable miles.

There is more information about qualifying miles and elite status in general on the FlyerGuide.com wiki:
http://flyerguide.com/wiki/index.php...W#Elite_Status

When WorldPerks eventually becomes SkyMiles, the same general theories and principals will apply, just with different names.