Modes work by introducing combinations of intervals that are tonic & different from each other. Lets say the chord of the moment is a maj6. Many Jazz players will start their solo on the 3rd or 7th of the chord of the moment. That immediately introduces an unexpected interval to the listener when the root is sounded by the bass. If the note following the 3rd is the 5th, the listener hears a minor interval which the soloist could not do, in key, when limited to the root of the chord of the moment. Likewise starting on the 7th following it with the 2nd. The audience hears a minor interval played over a major chord. Of course, things often get more complicated than that.
So to partially answer your question, modes work by engaging the audience in unexpected ways that often sound melodic & are in key. You are so accustomed to hearing it, the special nature of what is done doesn't impress you any more. It is there, nevertheless. Listen closely & perhaps write what you heard to better see & hear what is being done. JS Bach is the Father of modal composition. Perhaps you will find some Bach in your Library?
Hope that helps.