A vitamin C shower filter uses ascorbic acid - the same vitamin found in citrus - to reduce the chlorine in your shower water through a chemical reaction, converting it to harmless chloride. Most filters pair it with a sediment stage that catches rust and grit first. It works fast, which suits the hot, fast-moving water of a real shower. It does not soften your water, and how much difference you notice depends mostly on how hard and how chlorinated your water is.
Vitamin C vs. Activated Carbon
How the two technologies differ - and which one holds up at real shower temperature and flow.