You’ll start recognizing the effect that a minor 6 has, or the pleasant unresolution of ending a song on the four chord, or you may realize why you like or dislike a certain progression, etc. Practice listening to songs just counting up the scale as chords pass by and you hear that 95 percent of progressions are the one, four, five and six. Then just sing a regular major scale counting up: one, two, three, FOUR, FIVE, SIX (usually minor), seven then back to the octve of one. I’d suggest that everyone learns at least 4 basic chords to start with. So as a drummer I think understanding the number system may be even more useful for drummers than non-drummers cause we have to do it all in our head in a rehearsal setting. But because I have a rough idea of the number system, without even knowing what key we’re in I can say, “how about changing that five chord to a minor 6” or whatever. I have found that when I have chord ideas/suggestions in a band setting, I don’t have a keyboard in front of me to “test” out my idea or find the chord I’m looking for. I would say that these numbers literally tell you the relationship of chords and the musical effect of these different relationships. While I’m not a proficient non-drummer musician, I do play enough piano that I can often understand these chord “numbers”.