I live in the US, where property tax pays for local services and there's a good deal more devolution both at state and municipal level than there is in the UK.
Property taxes are calculated based on an estimated valuation of the property. There are exemptions based on age. You pay more for properties that are not your primary residence.
Services funded include the libraries, park district, police, and local schools. There are many more.
If you are living in a property valued at $1million, your taxes will be higher than properties of lower valuation, on a sliding scale. Higher valuation will result in higher annual taxes.
When you buy a house, the current annual taxes are included in the description so you know what you're getting yourself in for.
As property values rise, taxes do too, with different towns and cities in the county assessed at rotating intervals. You can file for a correction if you think your assessment has risen too much or of you think your valuation is based on incorrect information (like four bedrooms instead of three, more bathrooms than you actually have, etc).
Nobody is thrilled about property taxes, but everyone realizes that the quality of local amenities, especially schools, and crime stats, are big factors in maintaining or improving property prices, so you have to weigh what's important to you when you're buying.
Obviously, local control over spending, and local referenda over proposed increases to benefit various local agencies make property taxes more palatable.