The term "post-impressionism" covers a wide variety of different artistic styles. On a banal level, they are all post-impressionist in that they come after the movement known as impressionism, associated with the work of artists such as Monet. Impressionism sought to depict certain features of the objective world, albeit in a new and radically different way. Impressionists sought to capture the fleeting moments they observed in the natural world around them, using vivid colors and textures to achieve their intended effects.
Post-impressionists, on the other hand, were more concerned with expressing their subjective emotions. What mattered to them was the accurate expression of the contents of their souls rather than a depiction of the natural world.
Seurat can only really be described as a post-impressionist in that he came after the first wave of Impressionists. A more accurate description of his work would be neo-impressionism—that is to say, a new kind of impressionism. Strictly speaking, Seurat cannot really be considered a post-impressionist because he was still primarily concerned with depicting the contents of the objective world rather than simply subjective expression. At the same time, he departed from his impressionist predecessors in that he wasn't concerned with capturing the fleeting moment; he wanted instead to convey what was essential and enduring in the world around him.
He attempted to do this through a technique known as pointillism, which constructed paintings out of tiny colored dots. It is this preoccupation with color that Seurat shares with post-impressionists such as Van Gogh and Cezanne. But Seurat's intentions are different to theirs; he wants to use color to give us a more faithful rendering of the natural world, encapsulating its very essence.