Basically it set property tax rates at 1% of a property’s sale price and capped annual increases at no more than 2%.
The only time a house sees fair reassessment is when it sells...which means a lot of people end up sitting on land.
http://www.latimes.com/opinion/op-ed/la-oe-friedersdorf-prop...
"Perhaps most perversely, Proposition 13 has made it harder, not easier, to become a homeowner. California has one of the lowest rates of homeownership (55%) in the nation, second only to New York and nine percentage points below the national average.
The pernicious incentives that led to these outcomes are obvious in hindsight. With property taxes near frozen, local governments began to see residential development as a liability and commercial development as an income stream. For 40 years, that perspective shaped which new projects cities approved. Homeowners, meanwhile, had a disincentive to move if they had a low property tax bill locked in. Finally, these relatively low property taxes made California an attractive place to undertake speculative real estate investments and leave valuable parcels of land undeveloped."
One thing I'd add, is that Prop 13 also discourages any kind of mobility. For instance, my Mom often talked about moving to a different town, but she didn't, because her property taxes were so darn low. She's lived in the same home for over 40 years and if she relocated, her cost-of-living would go through the roof, due to higher property taxes.
https://www.zillow.com/homes/for_sale/19657362_zpid/
(See property taxes paid in the bottom Price/Tax History dropdown).
Cities in California (re)assess property values just like they do everywhere else. Go buy a house there and tell me that your assessed value is about right for a house in 1958.