The CoupleZabuHaku is the term used to refer to the romantic relationship between Zabuza Momochi and Haku.
Land of the Waves Arc
After becoming an orphan, Haku was left to live by himself in the streets. He then met Zabuza Momochi, who had "the same eyes" as him. Zabuza then proposed to Haku that, if he wanted to be trained and become his "Ultimate Weapon", he could come with him, which Haku readily accepted, devoting his life to become the ultimate tool for Zabuza.
Years later, Zabuza became a mercenary assassin for hire, and in one of his jobs he was hired by Gatou to kill a bridge builder, who was being escorted by Team 7. He had a brief battle with Kakashi and his team, but when Zabuza was about to be killed by Kakashi, Haku appeard and pretended to have killed him.
They later fight again, Zabuza battling Kakashi while Haku fought Naruto and Sasuke. After a long battle Zabuza was about to be killed by Kakashi's Raikiri (Lightning Cutter), but Haku appeared in front of him, receiving the fatal attack in Zabuza's place. Before dying, Haku grabed Kakashi's hand in hope that he could still be useful to Zabuza.
Upon not seeing any signs of remorse, Naruto lectured Zabuza about Haku's feelings and loyalty towards him, and that brought Zabuza to tears revealing that he did care for Haku. In a final act of repentance, Zabuza killed Gatou, at the cost of his own life. Before he died, Zabuza asked Kakashi to take him to Haku, and being by his side, Zabuza wished that he could go to the same place as Haku. Kakashi believed that they could go to the same place together.
Shinobi World War Arc
Both Haku and Zabuza were reincarnated by Kabuto Yakushi's forbbiden technique to fight the Allied Shinobi Forces. They meet Kakashi and as Kabuto erased their consciousness, they pleaded Kakashi to stop them, while Haku also stated that he had failed as Zabuza's tool, but Kakashi informed him that he had succeeded and that Zabuza did not saw him as only a toll but someone dear to him. That bought Haku to tears and he silently thanked Zabuza as the last of his consciousness faded away.
Later, with the release of the Impure World Reincarnation technique, a light of sorts encased Zabuza and Haku's sealed bodies as the technique was dispelled and their soul was returned to the afterlife.
- Haku devoted his life to be useful to Zabuza;
- After Naruto's lecture, Zabuza revealed to have feelings for Haku while crying;
- Before dying Zabuza wished that he could go to the same place as Haku.
Among the Fans
ZabuHaku is likely supported by the fact that both Zabuza and Haku showed deep feelings for each other. It's up to the fans interpretation to decide whether they had romantic feelings for each other or not.