It depends on what version the application in question needs.
If you've bought 10.6 then you can freely upgrade to any version in the 10.6.x tree. Right now that's 10.6.8. You can get this by simply running Software Update in the Apple menu.
If your application needs Lion/10.7 though, then you'll need to upgrade to Lion, which is a paid ($29) upgrade. You can get Lion once you launch the App Store in 10.6.8.