It means, that you are ready to give up a bit of what you want and accept a bit of what the other party wants. Simple example: you cook together with your friend and she would like to put a lot of salt into it, but you would rather have no salt at all. In this situation, if you would say: "Okay, let's put a little bit of salt into it", you would show Kompromissbereitschaft.

Du hast mit Jemanden einen Meinungsverschiedenheit, und ihr finde einen Kompromiss/Lösung Vorschlag mit dem beide einverstanden sind. To accept somebody's opinion and find a way who is good for everybody.

*Kompromissbereitschaft*