Gatekeeper is new security feature starting in Mac OS 10.8. See https://support.apple.com/en-us/HT202491 for more information about Gatekeeper features and benefits.
If you are unsure what version of the Mac OS you are running, see http://its.uiowa.edu/support/article/101460.
You can find Gatekeeper settings in System Preferences > Security & Privacy > General.
By default Gatekeeper will only open apps purchased and downloaded from the Mac App Store or from a list of “identified developers” that have been given the ok from Apple by obtaining an unique Developer ID. To install other apps, select the option to install from Anywhere.
Note: In most cases, Gatekeeper may only need to be disabled temporarily in order to install and initially launch an application. After that, Gatekeeper can be re-enabled to only allow applications from the Mac App Store and identified developers.