Quick answer: A filtered shower head reduces the chlorine and the rust, particulates and mineral deposits in the water that lands on your skin and hair. In hard-water, chlorinated areas most people notice softer-feeling skin, less limescale film, and less tightness or dryness after a shower. It does not soften your water and it does not change your skin directly - it changes what’s in the water that reaches you. Whether it’s worth it depends mostly on how hard and how chlorinated your water is.
Two things in ordinary tap water reach your skin and hair every day. Chlorine, added by water companies to keep supply safe, is a strong oxidiser - in a hot shower some of it leaves the water as vapour and the rest contacts skin and hair[12], and it reacts with organic matter to form disinfection by-products[6][7]. And dissolved hardness minerals (mostly calcium and magnesium) in hard-water regions[8][9].
Peer-reviewed research has looked at both: studies associate higher domestic water hardness and chlorine exposure with changes in the skin barrier[1][2][3], and hard water has been studied in relation to hair fibre strength[4][5].
What people usually notice is simpler: skin that feels tight or dry after a shower, hair that looks dull, and limescale film on the glass and tiles. A filtered shower head targets the water side of that.

