What happens if I turn off 'Cellular data' for an app?

I have the iphone 5s and i wanted to save data. Will anything change If i turned it off for like instagram, twitter ect?

Yes, that means no data so those apps won't do anything (unless of course you are on Wi-Fi, then they will work fine).

That would mean the app(s) would only be able to work on Wi-Fi, as far as their internet requirements.

All it means is you have to be connected to Wi-Fi to use those apps