QE is effectively creating money, which is then used to purchase financial assets in the hope that the person selling it will use the proceeds for something that is economically stimulative. It also reduces borrowing costs along the way.
Most central banks buy government bonds. As a result of this buying, the returns on these bonds are reduced and supposedly less attractive to the investors that previously would have bought them (or did buy them and then sold them to the central bank).
The issue is that an investor that previously would have bought a government bond, doesn't suddenly decide to spend that money in the general economy because government bond returns went down. They instead put it into other financial assets, like corporate bonds, the stock market, or perhaps real estate, thus driving a bubble in these asset classes.
In places like Japan, the central bank buys nearly all bonds issued by the government (effectively financing the government deficit). This distorts markets tremendously. Japan is the most indebted developed government in the world with close to zero GDP growth for 20 years and yet you need to pay them to loan them money for 10 years (i.e. negative return on their bonds).
As an investor, you currently have to pay the governments of most Western European countries to loan them money. In Switzerland for example, if you loan them $100 today, you'll get back $98 in 2 years and no interest. Even Spain and Italy which are in terrible shape fiscally, have a negative return on their 2 year bonds [1].
We now have extremely distorted markets. Heavily indebted governments around the world are borrowing money for free, enabled by their "politically independent" central banks. Some central banks are purchasing equities outright (Bank of Japan announced last month they would double their purchasing of equity ETFs).
There's also a great deal of research indicating that such QE policies increase wealth inequality, by driving up the price of financial assets (which are owned by the rich) and increasing the cost of living for everyone else that needs access to these assets (rent etc.) [2]
To most laymen, the idea that creating money and buying financial assets will somehow stimulate spending and inflation is clearly flawed. Central banks by design however, have few other options.
[1] https://twitter.com/MktOutperform/status/773577673587105792
[2] http://www.bloomberg.com/news/articles/2016-03-10/how-centra...