Usually with applications on the Mac, like Firefox for example, they come in a disk image with the extension .dmg. Once you open this, you'll notice a disk on the desktop with the name of the application on it. Open that disk image and you'll see the application icon in there with the instructions to copy that application icon to the Applications folder. Just a simple drag-and-drop.
What you've done is a common mistake by new Mac users: opening the disk image and running the application from the mounted disk image. One the computer is restarted, the mounted disk image is gone (since it's not really a physical disk) but the .dmg file is there, and they wonder where the app went (it actually went poofy with the mounted disk image).
This is usually something that people coming from Windows have a hard time understanding. On the Mac, the normal way is to copy the application icon to the Applications folder (or anywhere for that matter....it's really up to you...but common practice is to put it there in case you have other people using the computer and might want to use that application). That's usually how programs are installed on the Mac. Uninstalling is just as easy as taking that application icon, dragging it to the Trash, and emptying it.
Of course, not all applications tend to install this way. Others do include an installer and uninstaller, while others include an installer that can also uninstall the application when chosen from the installer application's drop down menu.
So to put it simply, do exactly what MisterMe said and you'll be fine. I just provided the explanation in case you wanted to know why this was the case.
