It gave them well executed little character arcs. Atleast Kobayashi and Tohru, that is, but even someone like Fafnir got a great line in here or there.
For something that is primarily a (somewhat romantic?) comedy show, every episode had atleast one scene where it slowed down and got a bit serious, sometimes even somber, and these scenes, throughout the season, painted a pretty believable picture of who Kobayashi and Tohru are. It made them feel like real people.
It's nothing revolutionary, but it's well executed, especially with how it culminates in the final episode.