Dan was a Hidden Leaf jounin, and Shizune's uncle. He always dreamed of becoming the Hokage after his little sister died. He cared for everyone in his village, and he wanted to protect all of the people in his village. He met Tsunade at a jounin meeting where Tsunade did her proposal to assign a medical ninja to each squad. Tsunade said it should be the Leaf's number one priority to efficiently train highly skilled medical ninja, develop a medical organization, and establish a solid structure for it. But because the Leaf was at war, the Third stated there was little time, they lacked the knowledge to do so, and the enemy wasn't going to wait for them. Tsunade became angry at the Third, and the only one that spoke out in favor of Tsunade at that point was Dan. Dan said he agreed with her idea and they should learn something from the past, and not let the sacrifice of the Leaf's fallen ninjas go to waste.
Both of them had a younger sibling that died in a raid on Konoha. And they both didn't want anyone else that was close to them to die anymore. Dan and Tsunade fell in love. And as a gift and a sign of luck, Tsunade gave him her necklace. The necklace that once belonged to her grandfather, the First Hokage, and the same necklace she gave to her little brother Nawaki right before he died.
But just like her younger brother, Dan died the day after receiving it. He was seriously injured in battle. Tsunade did everything she could to save Dan, but his wounds were too severe. Dan died on the battlefield, where his last words to Tsunade were that he wasn't ready to die yet, and he still had a lot of things to do. Tsunade, now having lost two people that are important to her, changed completely. She became afraid of blood, and left Konoha along with Shizune. Later on Orochimaru tried to convince Tsunade to heal his arms by bringing Dan and Nawaki back to life in exchange. A proposal which Tsunade ultimately refuses. She knows Dan would not have wanted to be brought back to life if the Hidden Leaf Village was to be destroyed in exchange.