A job order cost system is one in which a firm counts the costs for each separate "batch" of work separately. In other words, the company treats different jobs as separate things and therefore tracks the costs of each job separately from the other jobs. Because of this, a firm that uses this sort of system should be one whose jobs are not all the same.
For example, a car company that makes the same kind of car all day every day should not use this system. All its jobs are the same and so this system would not be appropriate. However, if a firm did many kinds of custom jobs (say, for example, publishing all sorts of different text books), it would be much more appropriate to use the job order cost system.
In short, then, the kind of firm that should use this system is a firm that does many jobs that are distinguishable from one another.