I must say all this talk about jobs and skills and spells taken from other classes is making me nervous. I've never played something similar so i hope i can figure it out fast. :)
At any given time you can be one of twenty main jobs, and then once you unlock your "support job," you can strap on any one of the nineteen other jobs you're not currently wearing at half level.
What this does is give you access to the spells, job abilities, and traits of the second job, augmenting your primary job. For example, my primary job is usually bard, but I'm almost always wearing the subjob of white mage because it gives me access to healing, buffing, -na spells to remove status ailments, etc. At the level my bard is at I really only need to sing songs once every three minutes, but with BRD/WHM I can contribute a lot more to the overall battle.
When I'm playing solo or farming, I'll be a job combo such as black mage/red mage, or thief/dancer.
In group play, subjobs can be highly variable. BLM/BRD is popular in small Abyssea farming groups because the black main mage has access to the 8 most important bard spells in Abyssea farming. BLM/WHM is good when you're in a group without a white mage. BLM/RDM is preferred when there's a separate white mage and a separate bard, because RDM's trademark is self MP restoration (from the spell Refresh and the job ability Convert), and by strapping on a RDM support job, the BLM has access to those abilities and is much more self sufficient.