There are different types of episodes; those that drive the story onward, those that give action or drama, those that develop character and setting. 'The Warriors of Kyoshi' belongs to the latter group.
There is development in all three main characters, so I'll just touch upon them one by one.
First, Katara. Her character is the least changing one, but there's still some development. Her feelings in the first part of the episode are unclear. It could be jealousy, or it could be resentment. However, her initial attitudes, including her not paying attention to Aang, chance to genuine caring by the end, a trait that keeps coming up and needs to be anchored at some point.
Next, Aang. Once the Kyoshi people find out that he's the Avatar, he finally gets the attention he wanted, and starts to like his destined role. However, he sees the superficial reasons for his popularity when his fans only want him watch him do new and exciting things. He realizes that the people who truly care for him, hi new-found family, are there for him. This is an important step for Aang, as he matures from a popularity-seeking boy who needs an ego trip to a responsible Avatar who will be able to face the oncoming dangers.
Last but definitely not least, Sokka. Of all the characters he undergoes the greatest change. In the beginning of the episode, his sexist thinking is once again demonstrated, much to Katara's chagrin. Later, when he meets the warriors of Kyoshi, he belittles them due to the fact that they are girls. Only after he gets humiliated does he realize that his view of the genders was very flawed. He accepts his mistake, and puts aside his sexist nature, creating a much more likable Sokka. Not to mention he also trains fighting with Suki, making him a decent warrior and a greater asset to the group.
This episode, though the pacing was a bit dragging, nevertheless warps the characters and lets them mature and prepare mentally for their upcoming task. A good episode that tweaks things right, where we see the characters grow and leave behind flaws, instead of coming into the story as 'better' people immediately. Make the whole thing more believable, and it probably makes the viewers connect to the characters much more.