What happens when a country cuts interest rates?

The first thing you have to know is that the adjustment of interest rates is the job of the Central Bank of a country in the case that the country has one- some small countries do not due to the high cost of running a central bank.

So, what happens when the CB of a country decides it needs to cut interest rates as has just happened in China recently? Since interest rate is the cost of borrowing, a rate cut spurs investment due to the fact that institutions/businesses can borrow at cheaper rates to fund expansion. More investment translates into more production, which translates into needing to hire more people, having to hire more people means increased wages, and increased wages leads to higher consumption. In this description it is evident how growth occurs if you are aware of the most basic, yet most important economic identity: Y = C + I + G + (X-M) where C is consumption, I is investment, G is government spending, and (X-M) is current account.

Furthermore, with the decreased interest rate domestic capital flows out to foreign countries (say U.S) where let's assume their own home interest rate is higher than that of China although our assumption is not necessary. This eventually translates into depreciation of China's currency relative to that of the U.S due to an increase in demand for USD with respect to the Renminbi.

Why might China benefit or even want a reduction in the value of their currency? Because their exports become cheap for major trading partners like the U.S and imports by the Chinese population become expensive. Through this medium the current account component increases real output (Y). For countries whose economy is export dependent therefore, cutting interest rate and the consequent depreciation of their currency that arises from that is one way to promote economic growth.