Basically, syntax is the rules by which signs are combined to make statements. If you consider the words of a language to be its signs, then its syntax is the rules which put signs together to make statements, ask questions, and produce other utterances.
Syntax incorporates the grammar of phrases, clauses, and sentences. Producing and uttering sentences is an important part of how we make sense of our world. We articulate the meaning of our experience in words; in the process of articulate, we make (or discover) the meaning of the experience. This process is similar to the ways in which we intrepret literature.
The syntax the exact structure of what we write is an essential part of its meaning. Change the structure and you have changed the meaning, at least slightly.
A few years ago, I was on Miami Beach. Along with the ocean breeze, there was the odor of exhaust from jet-skiers who were buzzing around just beyond the surf, coming close to swimmers and small craft. The juxtaposition of the two smells impressed me strongly. Since I'm inclined to express meaningful experiences in writing, I produced the following haiku:
carrying the fumes
of jet-ski exhaust
If it is successful, it will convey to the reader something of what I experienced. In any case, by articulating that experience in those words in that order, I discovered, formulated, and expressed the meaning of the experience for me.
Any writer does the same, thus the importance of syntax. If you think of syntax as the description of the living forms of language, rather than as the class room rules of grammar, you may find it more useful in developing your writing abilities.