The setting that says 'Allow applications downloaded from' are the Gatekeeper settings. Gatekeeper is there to stop malware from getting on your Mac, and that's a good thing. You can shut off this protection, though I wouldn't recommend it. This was the first time Apple offered Gatekeeper, and its default setting is 'Anywhere.') If you try to change the setting to 'Anywhere', the Mac will warn you against it (though it will make the change if you tell it to.)
The default setting for Gatekeeper on most Macs is 'Mac App Store and identified developers.' (The exception is OS X Lion 10.7.5.
Gatekeeper checks for the presence of a digital certificate embedded in the app itself that tells the Mac the app is from a signed developer who has registered with Apple. Given that reality, Gatekeeper helps OS X makes sure that app is safe to run, even if it's not from the Mac App Store. VPN Deals: Lifetime license for $16, monthly plans at $1 & more