The verb »entfernen« exists in two versions with two different meanings. (You also could argue it's two different verbs which are homonyms.)
- transitive
etwas entfernen
to remove something
Der Arzt entfernt den Gips von meinem Bein.
The doctor removes the cast from my leg.
- reflexive
sich entfernen
to leave, to go away
Der Soldat entfernt sich unerlaubt von seinem Posten.
The soldier leaves his post without permission.
You also might try to translate the last sentence as
The soldier removes himself from his post without permission.
I know, this doesn't sound like good English, but this is how to leave works in German.
So, the first two lines of that song text will correctly translate as follows:
Was auch da draußen warten mag
entfernt sich mehr, mit jedem Tag
Whatever may be waiting out there
moves away more and more every day (becomes more distant every day)
So, the answer to your question (What is going away?) is given in line 1: The thing that is waiting out there. This out-there-thing is moving away.
The song is about a person who travels around searching for something or someone, not knowing exactly what he is looking for, and the more he searches, the less he finds it.
The Emotion the song is about is »Fernweh« which is a German word that has no direct English translation. Dictionaries list as possible translations »itchy feet« or »wanderlust« (which btw is another German word, but it doesn't mean exactly the same as »Fernweh«). Another translation is »yen to see distant places«. But »Fernweh« is not really about being somewhere else. It is more about not staying where you are now.
Wherever you are, you always have the feeling that you miss something somewhere else. But when you're then somewhere else the »Fernweh« won't go away. You still have to move on, looking for something, not knowing exactly what you are looking for. You just know: It's not here, where you are. The more you move, the farther away goes whatever it is that you are looking for.
