The word "bond" can have quite a few meanings! The obvious, physical meaning is the noun; "the join between two or more objects", or the verb (which is based on the noun) "to join two or more objects together". The other meaning is "relationship", "the connection between two people", or the verb (again, based on this version of the noun), if you say that two people are "bonding", it means that they're getting to know one another. "Every bond you break" in your little song there means "for each relationship you end..." or "every person who loses your trust...".

As in, you had made a commitment to something or someone, but abandoned it. If you and I are close friends, we have a bond. If you betray me, you have broken that bond. In the song, it means a romantic bond, I believe.

the same meaning, it means every TRUST u break.