Dismantle the shower head, and scrub with an old toothbrush and vinegar solution. Let the shower head sit overnight in the vinegar to dissolve remaining deposits. If you did not dismantle your shower head you can simply attach a bag with a cup of vinegar for it to soak overnight.
Mineral deposits on your shower head are a sign of hard water. Mineral buildup is not only unsightly, but it can wear out metal fixtures more quickly, and can even lead to plumbing failure inside of your pipes. A water softener removes most minerals from water, but without one you are susceptible to all types of mineral buildup.