Explain What Council Tax Actually Pays For and Why Bills Differ Between Properties

The council tax bill arrives, is higher than last year, and does not explain itself. This explains what it actually funds, how bands are set and why neighbours can be in different ones, the reductions most people are entitled to but do not claim, and what to do if the band seems wrong. UK context throughout.

Explain council tax in plain English:
(1) What council tax funds and which local services it does and does not pay for; (2) how council tax bands are set and why two neighbouring properties might be in different bands; (3) the main discounts, exemptions, and reductions that most people do not apply for; (4) what to do if you think your property is in the wrong band.

UK context. One concrete example throughout. If any exemption is commonly missed by a specific group (students, single adults, carers), name them specifically.