Why you write S symbol for distance?

Strictly speaking, it's not. The symbol 's' is so often used for displacement because the symbol 'd' is often chosen for distance.

This is an important distinction in physics, where differences between scalar (distance) and vector (displacement) types are used to measure and describe different things.

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I believe that the standard explanation for the use of the letter s for distance is that the Latin Word for distance is "spatium". Whether s (or d) is used to indicate distance or displacement, the distinction is that a right-facing arrow is placed over the letter to indicate displacement since it is a vector quantity.

That said, it is probably not unheard of to find a textbook that uses d for distance and s for displacement, so long as their use is defined that way.