Quantitative Easing (QE) When a central bank purchases assets to boost the money supply. Whenever a central bank purchases assets it creates central bank reserves which improves liquidity in the market. Typically, in the U.S. the Fed will purchase long dated Treasuries and government backed mortgage based securities (MBS). Purchasing Treasuries raises the price of Treasury and therefore lowers the interest rates of the treasury1. Purchasing treasuries with central bank reserves was like printing a $100 dollar bill to buy another $100 dollar bill, it didn’t change the supply of money, just the composition of it (Treasuries -> Central bank reserves).
QE lifts financial asset prices because it converts Treasuries into central bank reserves. In turn, commercial banks hold more money in reserves and nonbanks hold more money in bank deposits. With the money in deposits, nonbanks are to invest in other asset classes such as equities or corporate debt1.
Massive QE is not enough by itself to move inflation higher, this has born out in the Bank of Japan, the Fed, and European Central Bank.