Job points coincide with experience points. Everytime your character attacks or uses a skill successfully during a battle, you earn experience along with job points. The more experience you get, the faster you level up. The same is with job points. The more JP you get, the faster you level up in that job. The highest level you can get for each job is 8.
You use the JP to learn skills. Lets say that each time you cast fire, you earn 21 JP. After about 10 casts, you would have more than 200 JP built up. From that you could learn another skill/spell, such as ice. When you have learned each spell for a job and are at level 8, you have mastered that job. In otherwords, you kick ass with that character.
If you are bored with this job or it is no longer effective, then it's time to move on. How? Go here to learn more: Requirements.
