What does it mean to sync apps to iPhone
This Apple Support article provides a quick summary of what syncing does. Basically, as XAlexOwnZX mentions, a sync copies applications, music, and other information between your iTunes account and your iDevice. This process backs up the content (apps, etc.) on your computer.

The advantage of syncing is that if your iPhone gets corrupted, you'll be able to restore it (or its replacement) to working condition, with all of the purchased content that is installed.

The disadvantage is that syncing takes time - however, with iOS 5, you can choose to sync over WiFi and you don't need to tether your iPhone to your computer.