The law of Supply and demand. When the Fed signals a willingness to pay above-market prices for bonds, the increased demand triggers an overall hike in trading price for bonds.
The same would be true if the government entered the housing market and began purchasing large numbers of homes at inflated prices - housing prices would rise.
The way this relates to interest rates is that bonds always trade at a discount of what they will be worth at maturity, based on the time value of money. The amount of discount is what determines interest rates.
For example, if traders will pay $90k today for a 3 year bond that will be worth $100k at maturity, that $10k discount implies an annual interest rate of 3.58%. If the government enters the bond market and drives the trading price of that bond up to $93k, the discount is now only $7K, which implies an interest rate of 2.45%.
So the Fed has lowered interest rates.
Gotcha
Inverse relationship.
Interesting.