Lord Syntax and Simple Sentences

Lord Syntax and his friend Nemesis sit a club to eat dinner. Lord Syntax notices that the piano player is playing the same tune all evening with a small variation. In the case of the piano player, different keys, chords, and tempos are used to create variation.

In the case of sentences, small variations exist also. The four variations on the simple sentence are given. What is syntax? Why is syntax important in the discussion of language?