Installing software on a MacBook
Generally application (.app) bundles are meant to be stored in /Applications of ~/Applications. I recommend using /Applications for the vast majority of installations, since the apps there will be accessible to other users' accounts`.

Application bundles aren't directly executable. Instead, their executable file is stored within the bundle (right click and select "Show package contents"), in {APPLICATION.app}/Contents/MacOS/

To open an Application bundle from the terminal, you can use the wicked open command with the -a flag, like: open -a /Applications/Application.app. This comes in handy occasionally, though I don't know why you'd want to open applications through terminal, rather than through the dock, dock stack, or spotlight.