Any significant relationship with an older woman is complicated for Katara, since it is overshadowed with memories of her mother. This doesn't stop Katara from forming relationships with older women - as for two years, that was the main population of her village. But those women who kept wanting her help or tsking at her for her bending attempts that often ended embarrassingly are very different than the relationships she's formed in Luceti and nothing could be farther from the case with this pirate thief.
Nami's very first conversation with Katara is marked with wonder on Katara's part - whoever heard of adventuring pirates? - and something that instinctively pleases the girl, being taken seriously. Their relationship received an instant boost when Katara and Toph responded to Nami's call for help over the journal to aid an injured friend. One of the best ways of getting to know a person is how they respond when kneeling in a pool of blood, and Nami responded to Katara's instructions quickly and calmly. After that, Nami took care to gently check up on Katara, and it was an interest that was eagerly reciprocated. Nami was the one Katara contacted when she figured out who the child!Sanji was, and Nami was the one who took Katara on her first shopping trip in Luceti.
After that... life got more complicated. Nami was kidnapped by Aku, Katara joined in on the rescue mission, and then Katara asked Nami to start giving her lessons with the bo. It's after this time that Nami's most outstanding characteristic occurs - her willingness to go and find Katara, confront her when she's wrong, and remain friends with her regardless of her decisions. That's a loyalty that Katara is not accustomed to finding outside of family members, and the fact that Nami offered it so simply and so consistently is something which stands out in Katara's mind as distinctly precious.
Nami
Nami's very first conversation with Katara is marked with wonder on Katara's part - whoever heard of adventuring pirates? - and something that instinctively pleases the girl, being taken seriously. Their relationship received an instant boost when Katara and Toph responded to Nami's call for help over the journal to aid an injured friend. One of the best ways of getting to know a person is how they respond when kneeling in a pool of blood, and Nami responded to Katara's instructions quickly and calmly. After that, Nami took care to gently check up on Katara, and it was an interest that was eagerly reciprocated. Nami was the one Katara contacted when she figured out who the child!Sanji was, and Nami was the one who took Katara on her first shopping trip in Luceti.
After that... life got more complicated. Nami was kidnapped by Aku, Katara joined in on the rescue mission, and then Katara asked Nami to start giving her lessons with the bo. It's after this time that Nami's most outstanding characteristic occurs - her willingness to go and find Katara, confront her when she's wrong, and remain friends with her regardless of her decisions. That's a loyalty that Katara is not accustomed to finding outside of family members, and the fact that Nami offered it so simply and so consistently is something which stands out in Katara's mind as distinctly precious.