"Monetary policy" refers to the decisions a government makes to control the amount of money flowing through the economy. It's not to be confused with fiscal policy, which is simply how the government manages its own money. A "contractionary" monetary policy is designed to reduce the amount of money in the economy, and there are times when this has distinct advantages. However, those advantages can quickly turn to problems if the money supply shrinks too much.
The single biggest advantage of a contractionary monetary policy is that it helps put the brakes on inflation, and the other advantages flow from that. Simply put, inflation is an increase in prices, and a little inflation is a normal aspect of a healthy economy. But when the rate of inflation gets too high, the effect can be disastrous.
Inflation can get out of control when there's "too much money" in the economy. If there are too many dollars chasing a finite number of products---or, more accurately, if demand for those products remains roughly the same but people have more money to spend on them---prices are going to rise. Contractionary monetary policy is designed to take some of the extra money out of the economy, so that prices increase at only a moderate rate.
What governments have to avoid is tightening the money supply so much that there are not enough dollars to go around. This can kill demand and knock an economy into recession.
Assume you have £13,000 in savings. If inflation is running at 10 per cent a year, but your savings are only earning 2 per cent interest, then that money is losing significant value with each passing day. Inflation punishes people for being prudent and actually encourages them to spend their nest egg while it still has value; a contractionary monetary policy encourages saving.
Protecting Standard of Living
Although wages tend to rise with prices---they are, after all, a "price" in themselves---they rarely keep pace once inflation really gets going. Even a 5 per cent annual raise is a pay cut if prices are rising at 10 per cent per year. The result is a declining standard of living as the same amount of work brings lesser rewards. A contractionary monetary policy protects your standard of living by helping your wages keep pace with prices.
The modern economy runs on credit, both for individuals and businesses, but inflation discourages lending, because the money that lenders get back in the future will be worth less than the money they lend now. To make a profit on a loan, lenders have to charge interest. The higher the rate of inflation, the higher the rate of interest---and there's still no guarantee that it will outstrip inflation over the long term. But there's an upper bound to how much interest a lender can charge, simply because the loan becomes too expensive for a borrower to afford. By keeping inflation in check, contractionary monetary policy encourages credit to keep flowing.