Fixed-exchange rates can definitely help with assuring investors and consumers of low inflation. If you say, you will trade 1 of your currency for x of someone else's currency and vice versa, then if you caused a lot of inflation, and 1 of your currency suddenly can't buy a whole lot, then people won't want to trade with you or your country anymore.
If you are wondering why central banks might not be automatically trusted to keep inflation down, consider the following.
Imagine a central bank making monetary policy. According to models along the lines of Lucas perceptions, creating inflation can stimulate an economy, but only in the short run when no one knows that the central bank is creating more inflation than expected. The idea is that firms will attribute the rise in prices from the inflation to higher demand rather than inflation, and will thus higher more people, lowering unemployment.
If the Fed kept trying to secretly keep inflation above expectations to keep unemployment down, you'd expect businesses to catch on, and the Fed in turn would have to keep raising their inflation target and...well, that's a disaster of infinitely rising inflation. In the 1970s in America, we had huge amounts of inflation (well, for us huge), until Paul Volcker decided to revamp central banking policy to more credibly target inflation.
Today in the good ol' USA of course, when the central bank tells everyone they are loosening the money supply to try to stimulate the economy, it has some effect on inflation. Why? Because the Federal Reserve can be expected to later tighten policy back down later when the economy is doing better, instead of falling into the above time-inconsistency problem.