Low Fed interest means you can't make good money safely by loaning it to the central bank. So it makes the alternative loans more attractive, mortgages are a relatively safe and profitable investment. When the cost of mortgages goes down the amount borrowable goes up so the people can buy more expensive houses. The immediate result is that their prices go up.

People tend to judge affordability based on repayments, not prices, so lower interest rates mean you can service a much larger debt for the same monthly repayment.

Where housing is scarce prices are determined by availability of credit more than anything else, so "you can" rapidly becomes "you'll have to, otherwise you'll be outbid by somebody who will".

Over the long term it's a shitty, negative-sum game for everyone except the banks.

Lower interest rates mean it's cheaper to borrow, which makes borrowing more affordable to more people, which increases demand, which increases prices when supply is limited (artificially or otherwise, see San Francisco).