A factory service manual ("FSM") is a service manual from the OEM (or original equipment manufacturer) that tells how to diagnose and repair a piece of equipment. Some vehicles (such as those from Nissan) are covered by a single model, while other companies (Honda, Mercedes-Benz) have several manuals per vehicle. They range in price from about fifty dollars up to hundreds.
The FSM differs greatly from an aftermarket service manual from a company like Haynes or Chilton. The first and most obvious difference will be the amount of material provided. Factory service manuals typically provide detailed and useful troubleshooting charts and a multitude of diagrams you will not find elsewhere. Because they are designed by the manufacturer they tend to be correct more of the time than the knockoffs and they often contain such complete information as manufacturer-intended torque specifications for nearly every bolt on a vehicle.
Another thing you will rapidly notice is the quality of the illustrations. Illustrations in a factory service manual are drawn to the proper size for the page upon which they will rest, and as such they tend to have uniform line weights throughout the book. Consequently the illustrations are always crisp and clean and will reproduce well when photocopied - highly desirable if you're going to be working with greasy hands. Illustrations in other manuals are generally enlarged or reduced and thus have varying line weights and usually poor quality, especially in the case of detailed diagrams where quality matters most.
In general, if you are going to do anything more than casual maintenance on your vehicle, you should have the FSM and not an aftermarket book. It is easier to use, has more information, and will tell you precisely what tools the dealer uses to work on the vehicle. Significantly older vehicles did not have complex service manuals, and the original factory manuals may not be available in any case, but on newer vehicles (anything from the 1970s or later) it is generally foolish to attempt a major repair without one.