A regimen is a systematic plan for some kind of therapy. If your doctor tells you to eat more vegetables, cut out potato chips, exercise, and take vitamins, he is prescribing a regimen for better health.
It's easy to confuse regimen with regime, which means a ruling government. Both words involve things that you follow. If you wash your face twice a day, apply medicine to your acne, and use a special lotion, that's your "skin-care regimen." A skin-care regime would be armed dermatologists taking over the government.