I think my favorite moments were when Cheren realized that power was all that was needed to be a Champion, and when Bianca came to terms with being a weak battler, and was ok with being the supporter for her friends. The character development with those two was incredible and awesome to watch unfold.
Cheren starts off as this big-shot semi-arrogant trainer who only wanted to be powerful and be the Champ. Very slowly he began to realize, that even though many of his opponents were his equal, he would only slightly overpower them, only because he couldn't see that the connection and bond between his opponent and their Pokemon is what made them strong. It took a final beat down on Victory Road for him to finally open his eyes to that fact, but he was never a bad guy or a jerk. He loved his Pokemon dearly, but never thought that by building his bond even further he would obtain the power he so craved.
Bianca on the other hand was kind of the exact opposite. Sheknew right off the bat she wasn't as strong as her two friends, but that never stopped her from trying. She continued her way through the region by her friends' sides and kept battling and getting stronger in order to help them when needed. When the disaster at Victory Road happened, she wanted to help so much, but realized that she would only get in the way with her current power, so instead, she did whats he knew she could and that was support her friends by asking the Gym Leaders for help. Her love for her friends is what her strength lies in, and she used it better than anyone has ever before.
Plus there's a ton more detail I'm basically skipping out on because it's all too much, but these two were definitely a big point for me in Black and White.