Lin (Full name originally Linda Amelia Anderson, now Garmadon) is a Master of Wind. Breeze is a nickname of hers.
Lin grew up in a village near Ninjago City. She lived an average life until a master of dark magic by the name of Master Zhan took over the village. With a band of skulkins that had rebelled against Garmadon's control, he killed Lin's parents when they resisted.
Lin, though generally timid, was angered and became a ninja, resolving to defeat Zhan. Though she had yet to discover her element, she made a gi, armed herself with twin daggers, and created the nickname Breeze to hide her identity. She made two friends, Alice, a Fire ninja, and Tanya, a master of the Mind.
Her fight with Zhan ended in him being sucked into his own portal. Some time after that incident, she began to regret her actions, her friends left her, and she left behind her ninja ways, going by Lin again.
Lin met the ninja in between Seasons 2 and 3. She trained with them in an attempt to further unlock her ice powers, but to no avail. She originally had no interest in being a ninja with them, but as time went on, the idea grew on her.
In Rebooted, when Zane sacrificed himself, Lin was heartbroken, shutting herself away from everyone. Then one day she found a way to open her pendant, and its contents revealed that she was a master of Wind. She made use of her alias Breeze and her gi again when secretly entering the Tournament of Elements. It was not until later that she revealed herself to the ninja. Breeze also came face to face with Clouse, who said Zhan was his brother. Zane, who had just escaped, rescued her. From then on she was considered one of the team, and generally went by Lin once more.
Alice and Tanya - Though they helped Lin get into Zhan's house, and they all had a mutual respect for each other, Alice was forced to go back home, and Tanya didn't want to be a team after that. The two never actually knew Lin's real name.
Zane - After rescuing her, the two became very close... Yes, yes, you can ship.
Morro - Lin and Morro are cousins, both being masters of Wind. Because of this relationship, the two promised not to fight or hurt each other.
Misty - Lin and Misty are old acquaintances. Zhan arrived and Lin defeated him while Misty was away, and when she came back, she was furious over Lin's new attention. She later comes back in the third of Lin's stories to destroy Lin and her friends with her newfound Nebula powers.
Michael - Michael has a huge crush on Lin, which Lin accidentally encouraged. When Michael learns of Lin's location, he finds her in Lin's third story and a lot of awkwardness ensues.