This page doesn't contain spoilers beyond what is revealed early on in the book (and at Nie Huaisang's introductions in both timelines).
You most likely already know this if you're here, but just in case: Jiang Cheng and Nie Huaisang are important secondary characters in the danmei novel Modao Zushi (MDZS) by Mo Xiang Tong Xiu, and obviously in the various adaptations.
MDZS is not told chronologically. There is a main story, after the protagonist Wei Wuxian's resurrection after being summoned into a body that is not his, thirteen years after his death. This story is interspaced with flashbacks to events in the past. Those flashbacks are themselves not in chronological order. Some of them are Wei Wuxian's memories from his old life, from his childhood, adolescense and up until thirteen years prior, when he died. A few others are from the time after he died (in the interest of brevity, let's see these flashbacks are accessed through supernatural means).
Aside from a short introductory chapter, the book starts with Wei Wuxian's resurrection. At this time, Jiang Cheng and Nie Huaisang are the leaders of two of the story's four most powerful cultivation clans.
Jiang Cheng Courtesy name Wanyin
In the "present", Jiang Cheng is the leader of the Jiang clan of Yunmeng. He is a powerful man, prone to anger, and he is feared and respected. He holds a grudge against the dead Wei Wuxian, and is always on the lookout for people that might be Wei Wuxian come back to life. He does not treat these people kindly.
At the start of the past timeline, Jiang Cheng is the son and heir of the Jiang clan. The main character of MDZS is Wei Wuxian, the head disciple of the clan, and Jiang Cheng is his shidi.
Shidi is normal translated as martial younger brother.A lot of the fandom interprets Wei Wuxian and Jiang Cheng as adopted brothers , but that isn't really what it means. It means that they are both disciples of the same teacher.
Nie Huaisang is, in the present, the leader of the Nie clan clan of Qinghe. His clan was very respected in the past, when his half-brother was clan leader, but Nie Huaisang has a reputation for being indecisive, weak and ineffectual, which has also lessened the Nie clan's reputation. He relies on his older brother's sworn brothers, Lan Xichen and Jin Guangyao, themselves the leaders of the other great clans.
When they were fifteen, Jiang Cheng and Wei Wuxian were sent to live at the Cloud Recesses, home of the Gusu Lan clan, to train and study under Lan Qiren, as was the custom for prominent cultivation families. Nie Huaisang was Jiang Cheng and Wei Wuxian's friend and classmate from when they were at the Cloud Recesses.