Mastering a champion in league of legends is just like learning a new song on an instrument. A champion has certain timings and rhythms to the way they play. The auto attack animation, the ability animations, the combos, and the spacing.
Going into practice tool and getting a feeling for these timings is key to mastering a champion. See how there is a rhythm to the auto attack of a champion, just like the tempo of the beat in a song. The note is the beat where the music is played, where you auto attack, and the space in between is where you move. So mastering a champions auto attack is hitting that beat perfectly while having no downtime on your movement.
That is why players who master their champions have a certain elegance in their play, because there is no wasted space and each movement is precise.