Singing is a Bard's main Magic skill, and it determines how effective songs are. By equipping different kind of instruments, Bards can level their Singing skill as well as their skill with the related type of instrument.
Only Bards and other jobs with Bard as a Support Job will have the ability to use songs as magic, but even being the only viable job for this skill, the skill cap is a modest C rank. The String and Wind instrument skills are only increased by playing string or wind type instruments, which cannot be equipped by anyone but a Bard. Even characters with Bard as a support job cannot equip instruments. The Bard also has a C rank in both Wind and String instruments.