Why do central banks print money? If a country's central bank prints money, it causes inflation. However, apparently, small amounts of inflation is a good thing.

Why is the case? What would happen if central banks stopped printing money altogether (except to replace destroyed bills)?
If a central bank stopped printing money then deflation would eventually occur meaning the value of $1 would increase over time. 

There is a simple intuition as to why this would happen. Imagine there is an economy where the only product either produced or sold is widgets. Lets assume that the central bank fixes the total amount of currency in the economy at $1,000. Lets also assume to keep the math simple that every widget produced every year is bought and consumed and that people in this economy don't ever save money and spend 100% of their income every year on widgets (this is a dubious assumption in real life but makes the math easy, it is a fair assumption in real life that citizens will spend a certain % of their income on goods and services every year that are consumable).

If the economy produced 100 widgets per year based on its level of production and those widgets were bought using the available currency then each widget could sell for $100. 

Lets now say that due to population growth and increases in technology the economy can now produce 200 widgets. There is only $1,000 to buy the 200 widgets so each widget now sells for $50. 

The price level has halved. In order to buy the same product (1 widget) you have to spend half as much money. If the central bank wished to keep price levels the same they would have to increase the money supply to $2,000 to keep up with he increase in productivity. This is why you expect a central bank to increase the money supply over time.