The mechanism is straightforward: paying points upfront reduces the ongoing interest rate, which lowers the monthly payment for as long as the buydown applies, often for 1 to 3 years on a typical product. Whether that upfront cost is worth it depends on how long you plan to keep the mortgage at that rate.
A builder-funded buydown works the same way but is sometimes used to make a new-construction listing look more affordable on a monthly basis, so it is worth confirming whether the price itself reflects that incentive before assuming it is a straightforward discount.
A mortgage broker can run the actual numbers for your situation better than a general rule of thumb. Get your hand-reviewed valuation from Joel Dyck.