Kopfsprung is a fantastic example of a German compound noun, literally a 'head-jump' from Kopf (head) and Sprung (jump or leap).
In the song, it's used as a powerful metaphor for total trust and bravery. The line "Ich folg' dir in jeden Sturm / Kopfsprung vom Zehn-Meter-Turm" (I'll follow you into any storm / a headfirst dive from the 10-meter tower) creates a vivid image of taking a courageous leap of faith for someone you believe in.
This song is a massive pep talk, a real anthem for self-worth! Sarah Connor sings directly to someone who's fighting their own battles, telling them to put their "Rüstung an, auf in den Kampf" [Armor on, into the fight]. It's about ignoring the haters and the pressure to be a certain way. She even calls out the old-fashioned advice people give, like "‘Steh deinen Mann’, sagen sie" [“Be a man,” they say], and flips it into a message of strength.
The whole point is that your value isn't about what other people see. It’s for the moments "wenn die Lichter aus sind" [when the lights are out] and there's no applause or makeup. That's when you're told, "Bist du das schönste Mädchen der Welt" [You are the most beautiful girl in the world]. It's a powerful reminder that you are enough on your own, you don't need anyone else to complete you, and you should never, ever forget it.