In an inflationary regime, money becomes one of the least valuable assets you can own. A ton of steel bought today will still be a ton of steel in a month, but the $750 that buys a ton of steel today won't be enough to buy a ton of steel next month. Assets have their own depreciation and costs of ownership, but the greater the rate of inflation is, the more attractive everything else looks compared to money.
Banks, of course, have piles of money, and they would like to charge as much interest as they can to lend it out (that's how they make money on money). But lending is a market; banks with lower rates will attract more borrowers, and banks with higher rates will attract fewer. So they cut their rates in order to attract borrowers who will hopefully invest their money in something, make a return, be able to afford to pay back their loan with interest, and make the bank at least a small profit. Whoever doesn't cut their rates is left sad and alone with a steadily devaluing pile of money. In a low-inflation or deflationary situation, the bank doesn't feel so bad about holding on to a pile of cash (or treasury bonds), so demand from borrowers is able to drive the interest rate up.