The PSA makes the first slice of savings interest tax-free: £1,000 for basic-rate taxpayers, £500 for higher-rate, and nothing for additional-rate. Low earners may also get up to £5,000 of interest tax-free under the separate starting rate for savings.
The PSA has been frozen since 2016 while interest rates have risen, so ordinary savers with five-figure balances outside ISAs now breach it routinely; HMRC collects the tax by adjusting tax codes or through Self Assessment. Check your exposure with the Savings Interest Tax Calculator, and shelter what you can in an ISA.
£25,000 in an easy-access account at 4.5% earns £1,125. A basic-rate taxpayer pays 20% on the £125 above the £1,000 PSA, just £25; a higher-rate taxpayer pays 40% on the £625 above their £500 PSA, £250. The same savings inside a cash ISA would owe nothing, which is the whole argument for using the wrapper.