Welcome to Android Central! What phone do you have? Did you turn off Auto-sync, or did you restrict background data? They're two somewhat different things.
To turn Auto-Sync on, you can go to
Settings>Data Usage, tap the Menu button, and check the Auto-Sync box. It's generally easier to turn Auto-Sync on and off if you use a toggle widget on the homescreen. Most phones come with the Power Control toggle bar, which includes an Auto-Sync toggle, and there are lots of other widgets you can install from Google Play that do the same thing or are more versatile. My favorite is
Power Toggles.
The Restrict Background Data checkbox is in that same menu I mentioned above. If you check it there, I'm not sure if it restricts the background data refresh of all apps or only some. You can individually restrict background data for a particular app by selecting an app in the Data Usage screen, scrolling to the bottom, and checking the Restrict Background Data box if present.