When trying to run Eclipse for the first time after downloading it from the Eclipse Download Site the following errors occurs as show in the screenshot:
Eclipse.app Cannot be opened because it is from an unidentified developer
By default Mac OSX security is set to only allow to run Apps downloaded from the Mac App Store or Developers that are known to Apple. If you try to install and run any App that does not meet the that criteria, the above error occurs. In order to fix this go the Settings -> Security and Privacy section.
On that screen most likely the 2nd or 1st option would be selected, which does not allow Eclipse to run. So select the 3rd option(Anywhere) as show in the below screenshot. Now go back and launch Eclipse, it should now be able to run.