It's a mounted Disk Image [.dmg]
You should be able to right-click inside that window [over some empty space] & "Eject Brackets Release 1.14".
It should then not re-mount automatically. You can also simply discard the .dmg file once you've installed the app, by dragging to your Applications folder as indicated.
Any Application delivered by this method should be run only after copying to Applications & not from the mounted Disk Image itself. If it is running from the image, it will not let you eject.