These executables may have to be copied to a "special place" such as the Applications folder, to execute correctly.
If this is a requirement, the developer will often include an Alias of your Applications folder in the .dmg, and dragging the Application to that Icon copies the application to your Applications folder (after authentication with an Admin user_id and password).
Q: You ARE use to downloading apps from place like http://www.macupdate.com and then dragging them to Applications (not all of them have an alias showing to make it so anyone can)?
From the Dock if you click and hold on Dock icon alias - Show in Finder which of course opens the Application folder
Just do a "Command + Shift + A" will open the Applications folder in the Finder, then drag the application to there.
Most Windows apps are called "executible" but people rarely refer to a Mac OS X that way. As app as a program, and apps are "packages" - if you click on one and do Get Info it will show as... a folder and contents and subfolders.
But Windows apps don't come on DMG (mountable disk images) and because they are not or should be be anything but "read only" you cannot run an application from one. They have to be copied to where they can be launched and write to disk, adn write to the Preferences folder.
I must be more exact. It is not a simple dmg file, it is a sparseimage file. The apps that are on on sparseimage did run before. I did did not use it for a while and was surprised when the apps did not run. I upgraded to Mountain Lion before I noticed the change. it seems that the sparseimage has some "do not run anything inside"-flag.
When I copy one of the apps to a different place, i.e. application folder, it does run again.
Well yes you can do more things - and we are not mind readers so assumed it was an app that was shipped and downloaded for installation.
Rosetta is gone. PowerPC apps are history now and won't run as of 10.7 and up.
And when upgrading to ML or Lion, a clean install avoids problems works better and still allows for Setup Assistant to import what it can from your old backup / dual boot / system.
SL can also be run in a VM like Fusion or VirtualBox or Parallels or some people use SL primarily - some went back because ML doesn't add and the removal of Rosetta.