While the definition of health has some objective and universal aspects, it also has aspects that can differ with culture. It is something of a hybrid of these two.
Of course, all cultures would agree on certain aspects of health. Clearly, someone who is wasting away and dying from an incurable disease is not healthy. Similarly, someone who has gotten a fever and is delirious, or who has a festering wound that has led to gangrene is not healthy. These are things that all cultures can agree on.
However, there is also an aspect of the definition of health that is more cultural in nature. In a sense, we decide what is normal and what is not normal as a society. The different ways in which we define health are sometimes set by cultural values. For example, there are places where obesity is seen as desirable because it shows wealth. In the US, tanned skin is prized and is seen as healthy even though we know it brings the risk of cancer. Sometimes, our definitions differ because of our levels of medical and scientific knowledge. In a less developed culture, a person of 50 who has a hard time walking might be seen as healthy for their age because everyone in the society has to do hard physical labor and therefore ages quickly. By contrast, we in the US expect people to be physically active into their 70s and beyond and we would say people are not healthy if they cannot do this.
Thus, there are aspects of our definition of health that are universal and other aspects that are not.