People with a compromising conflict style look to meet in the middle. They are willing and capable of hearing out the other side, but will not necessarily dive in to understand motives and deeper concerns. They value quick resolution and will give up on some of their goals to achieve it. They sometimes avoid conflict altogether if they don't really value the thing they're fighting for and other times will be more assertive and obstinate when they think the other party is not being fair. This conflict style is particularly useful in situations where an expedient outcome is favorable and you're not so emotionally invested that you will feel immense resentment should you lose some ground.
There's an old adage that "a good compromise is when both parties are equally dissatisfied". This tends to be case with a compromising conflict style. While you might think that each party making a tradeoff would lead to harmony and show care for the other person, it can instead lead to a slow accumulation of resentments that don't really address underlying concerns.
For instance, a conflict might arise if you are very tidy and your partner is not. A compromise without a "why" might involve you cleaning up the house in exchange for your partner doing another chore. Asking why might reveal something deeper. Perhaps you want a tidy home because you feel chaos in your life and they can help you temper that chaos in other ways. Perhaps you feel underappreciated when they don't help you clean. Perhaps they are messy in defiance because they feel you are trying to change them. Why resolves deeper conflict. What resolves immediate conflict.