Short and long term interest rates in this case are for US Treasury Bonds that mature at different lengths of time. Short term bonds tend to have lower interest rates since you're taking less risk that your money will be tied up when the economy grows at a faster pace. If you invest in long term bonds and the economy hits a growth spurt, your money is stuck for a much longer period of time earning less interest than if you had invested in something other than that bond.

Edit: Missed the first question in your post. The Federal Reserve is essentially buying fewer Treasury Bonds when the bonds it currently holds matures. Instead of reinvesting the payoff + interest that it received for those bonds, it is now just taking that money and essentially keeping it out of circulation.

GP meant "reducing balance sheet". When the fed buys long term bonds it issues short term debt thus increasing its balance sheet and incidentally reducing long term rates. During the great financial crisis, the fed bought a lot of long term debt increasing its balance sheet to levels not seen since World War 2. It is currently in the process of reducing its balance sheet which should have the effect of increasing long term rates, but they aren't responding as much as predicted. This is why some people fear a recession.

There are many other factors, but it should be noted that this is the longest time of a financial expansion (time since the last recession) in modern history. In the 70s and early 80s there were 4 recessions in a 12 year period.

I meant balance sheet but mistyped, sorry about that