The characters combine almost like a direct, literal translation of the English chemical name “para-acetylaminophenol”, which is the systematic name for acetaminophen. It's a great example of how modern scientific terms were constructed in Chinese using existing characters to represent chemical concepts.
The term “对乙酰氨基酚” itself holds no deep cultural meaning, but its use highlights practical aspects of modern Chinese life and healthcare. In China, like in the West, there's a distinction between a drug's generic (chemical) name and its brand name. While this long chemical name is required by law on all packaging, the general public overwhelmingly relies on brand names (e.g., 泰诺 Tàinuò for Tylenol, 芬必得 Fēnbìdé for a popular ibuprofen brand) or simple descriptions of what the medicine does (e.g., 止痛药 zhǐtòngyào - “pain-stop medicine”). A key cultural point for a foreigner is the role of the pharmacy (药店, yàodiàn). It's very common to walk into a pharmacy, describe your symptoms (e.g., “I have a fever and a headache”), and have the pharmacist recommend a product. They will likely hand you a box where you can see “对乙酰氨基酚” listed as the active ingredient, but they will refer to it by its brand name or function. This contrasts with some Western cultures where people might be more likely to self-select a familiar brand without consulting the pharmacist.
This term is used almost exclusively in formal, written, or technical contexts.