What does a high band mean in blood work?

Fighting infection. "Bands" are immature white blood cells. When the body is under significant attack by an invader (bacterial, viral, or otherwise), it calls out the Marines (white blood cells as key portion of your immune system) and cells released a little early into circulation can be identified as such and are called "bands."
Infection. That there is a higher likelihood of a bacterial infection as opposed to viral. .