Everyone has felt the feeling in which when you are looking at something so beautiful, so majestic, so awe-inspiring, that you realize you have stopped breathing, if only for a few seconds. This is what it means to be breathtaking. It means that it literally takes your breath away.
Something breathtaking can be extremely exciting, beautiful, surprising, remarkable, or astonishing, that it is a marvel to behold. Something that is so gorgeous that the breath is knocked out of your lungs just by looking at it. For example: The view was breathtaking.
However, not only good things can be breathtaking. The term can also refer to something that is so bad or shocking that it stuns you; when you are so surprised that the breath is knocked out of you. For example: Her rudeness was breathtaking.