Clarification on Bard instruments

[Zehrikrom]

I noticed that instruments can't be used while wielding a weapon, so I usually just melee things to death while singing. This works fine so far, but I assume instruments serve some sort of purpose. I checked the wiki, but most guides were about kiting.

Anyway. My question is this: How do instruments affect songs, and when should I use an instrument vs. a weapon?