What is Post-Impressionism
Post-Impressionism was the style that developed out or reacted against Impressionism. Post-Impressionism is situated in the late 1800's and early 1900's.
Similarities between both Impressionists and Post-Impressionists are: a real-life subject, distinctive brushstrokes, thick layers of paint and vivid colors. The main difference between both styles is that Post-Impressionism aimed to attain more form and structure, as well as more expression and emotion into their paintings.
Pointillism and Divisionism both are subdivisions of Post-Impressionism. Out of Post-Impressionism developed such art movements as Cubism and Fauvism.
Pointillism / Divisionism
The artists interested in this new way of painting, studied the different optics of colors. As opposed to colors that blended in (=impressionism), the pointillism used little dots in pure colors. When moving further away from the painting, the different points start blending in together into one coherent picture.
At first the new artistic style was named divisionism, but now it is mainly called pointillism. Technically, divisionism is the theory and pointillism is the technique, but people generally refer to this style as a whole as pointillist.
Pointillism was, unlike impressionism, very theoretically grounded. Often different versions had to be made and it could take the artist up to a year to get the result he wanted. This by no means represents the "quick impression" that impressionism tried to attain.