As the fed buys bonds, it raises the price which lowers the rate.
As rates are lowered for things like mortgages and corporate bonds, people and corporations have more money to spend. Which they do generally spend which stimulates the economy.
Lower rates also cause corporations and people to borrow more which in a fractional reserve banking system actually creates money out of thin air. The reason why corporations borrow more is because with a lower WACC (weight average cost capital) they can invest in more projects (I.e. spend money) for any initiative that has a positive NPV.
All this results in higher wage expectations due to people expecting higher wages based on higher prices (gasoline, cars etc) which moves the fed money to people's hands and increases the prices of consumer goods including fmcg like TP.
As you can see there is a long link from cause to effect which is why we are seeing the slow increase in inflation. In many sectors like agriculture this is not even priced in yet as they are ultra competitive. But as their inputs go up (people and raw materials, hardware ), they will also have to increase prices.
Even when eventually fed raises rates or tapers their buying, prices once gone up have a way of sticking around unless efficiency improvements like automation reduce input costs.
Scenario 1: Fed buys $20 billion of corporate bonds per month from Microsoft.
Scenario 2: Fed does not buy $20 billion of corporate bonds per month from Microsoft.
Consider all other things being equal, in the first scenario Microsoft's borrowing costs are drastically reduced. This means that Microsoft has more money. This means that Microsoft is able to hire more people, that the people that work for them get larger bonuses because they are typically tied to the profitability of the company.
This puts more money into real people's hands to buy toilet paper and golf clubs. That then multiplies throughout the economy. Suggestions for additional reading if you are really interested in these things:
1. Money Multiplier
https://www.albany.edu/~bd445/Economics_350_Money_and_Bankin...
2. M1 vs M2 money supply
https://www.investopedia.com/terms/m/moneysupply.asp
3. Fractional reserve banking
https://www.investopedia.com/terms/f/fractionalreservebankin...
4. Fed open market operations
https://www.investopedia.com/terms/o/openmarketoperations.as...
Example: Joe just had a kid and was going to buy a house in a good school district no matter the cost. With a higher mortgage rates, he'd have wound up house poor for a few years. With today's rates, he has a comfortable savings rate. Since he's not scrimping, he decides this month he'll buy that putter he'd been eying.
