Select the application, and right click for Get Info.
What application name, version number, and other details do you see?
As pointed earlier, it could be that the application requires a different (higher or lower) version of OS X than you are running. It could be that it is is for a different platform, or that it was copied incorrectly from somewhere else, there could be some corruption in the file, ... a number of options. There also could be 'locked' selected for some reason in the info window. The version number matters as different versions of different programs have different needs of OS and hardware, it could be the frameworks not compatible with the version you try to use... more details would be useful.
Right click in Finder for "Show Package Contents" shows the content in a new window. So inside the application there is Contents folder, and inside it you would typically see at least the folders MacOS and Resources. In MacOS folder you usually find the executable for that application. Is there anything in MacOS folder for this application?
Where is the app located? Applications folder or somewhere else?
If nothing appears to happen, open Console and look at what it says when you try to open the app once more. Perhaps something is missing or has been moved.