I am unabashedly in love with Doctor Who. And surprisingly, it's almost never about the Doctor himself, but rather his amazing companions: Rose Tyler, Jack Harkness, Martha Jones, Donna Noble, River Song, Rory Williams, and this clip's star, Amy Pond. They are some of the best written characters on television and masterclasses should be done on their development.
What it takes to understand this clip (hey, great writing is great writing!) is that the Doctor has rewritten the universe, but only by sacrificing his very existence. If only someone can remember him, he can return. I won't spoil any more of the series for you, but here you go - a lesson in how to use a trite saying and give it a fantastic emotional heave.