The best way to explain it, is to point out that all notes have some bass in them. This is why a concert grand piano sounds fuller, richer than a upright spinet piano. If they are both playing middle C (or any other note) you would think they would sound the same, but they don't. The large enclosure of the grand piano resonates fuller. This sound you hear encompases a larger frequency spectrum than the middle C being played. The same is true for all instruments. For that matter, all musical instruments would sound exactly the same if all you heard was the same middle C. It is the sound surrounding that note that makes all instruments sound different.
Your speakers don't have a problem playing the high frequencies; the tweeter does not need a big cabinet to resonate. The bass is always the problem. The sub fills in the lower part of that frequency spectrum.
This also explains why a large room has a sound different from a small room. You can feel it when you walk into a large room (or hall) more than hear it.
You will notice much more than bass by adding a musical audiophile sub. You will notice more "air" or "space" between instruments because you are hearing the full spectrum of sound. That grand piano will sound more real. So will flutes, oboes, violins, drums, guitars, etc.