A pinstripe is a decorative pattern typically found on men's suits that is composed of very thin vertical stripes that run in parallel to each other typically in fixed width intervals. Pin stripes can either be dyed and painted onto the fabric or sewn into the fabric with thread.
Traditionally pin strips were seen as a hallmark of conservative formal business suits worn by men who worked at a company that expected their employees to project a high degree of professionalism and refinement. While this is still true to some degree, pin stripes can now be found on many different types of suits and are now more popular as a fashion decision then a statement. Pin stripes are not relegated to simply appearing on suits, they are found on many dress shirts, pants and even uniforms as a form of decoration.
When matching a pin-striped suit to shirt and tie, make sure to alternate the size of the patterns on each piece of clothing. For example: A suit with very narrow pin-stripe pattern would combine well with a wide striped necktie. Wearing different types of patterns on each piece of clothing is a great way to add more style to an outfit. If done correctly, it shows, besides having a large wardrobe, one's understanding of elegant style. To read more on this subject you may also want to read our guide on Shirt and Tie Matching
Pin stripes on neckties do exist but they are no longer called "pin striped" but pencil striped ties.