.exe is a Windows executable so it will run on Windows only.
.app is an OSX application, I believe.
.jar is a Java archive, which in this case is presumably an executable Java archive. This should run on any OS which supports Java, as long as Java is installed. If your system doesn't support Java, then you can't really play Minecraft, can you?
So if you have Windows, download the EXE. If you have OSX, the APP should work (if not, then the JAR should work). If you're on another OS such as Ubuntu, you must use the JAR.