How to understand a constant valued surface?

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Often in physics my textbook refers to a "surface of constant X" where $X$ is some quantity like temperature, pressure etc.

However, it goes on to refer to the gradient quantity $\partial_i X$, where $\partial_i$ denotes the derivative with respect to some spatial coordinate. I don't understand why this derivative is not just $=0$?

I think my confusion is related to the definition of a level surface e.g. this question, but having scoured the available answers I still do not quite understand.