In Chinese culture, family lines and relationships are defined with much greater specificity than in most Western cultures. The English term “father-in-law” is ambiguous; it could be your wife's father or your husband's father. Chinese makes a crucial distinction.
This distinction reflects the traditionally patrilineal structure of Chinese society, where a woman “marries into” her husband's family. The terms for her husband's parents (公公, 婆婆) are different from the terms a husband uses for his wife's parents (丈人, 丈母娘). A good Western comparison is the difference between a “paternal grandfather” and a “maternal grandfather.” While English speakers often just say “grandpa,” the more specific terms exist and highlight which side of the family is being discussed. In Chinese, this level of specificity for in-laws is not optional; it's the standard. Using the correct term shows you understand and respect the family structure. This relationship is built on respect (尊敬, zūnjìng). While the son-in-law is not part of the 丈人's direct family line, he is expected to treat his father-in-law with the same respect and care as he would his own father.
While 丈人 (zhàngrén) is the correct term, how you use it is critical.