A country that can sustain a low inflation rate is likely experiencing good economic times. The people have confidence to go out and spend money for the things they need and are not "squirrelling" it a way for expected bad times.
It means that the economy is good, people are confident, and mostly they are employed in jobs that earn them decent wages. They keep more of their money (instead of being taxed into submission). As a result, they spend more and in turn, stimulate the businesses in their area, thus increasing economic growth.
Low inflation says that a country has prospered economically and that the standard of living is good. It says to me that there is little government intervention and free enterprise is healthy. It also says that most people are well employed and making good wages. It probably says taxes are lower and commodities are cheaper.
Although not the perfect indicator of a country's economic status, low inflation paints a pretty accurate picture overall.
The previous posts really explained things quite well. If I could stretch the analysis out into the political and social realm, I think that this trend indicates that there is a sense of prosperity and political stability in the country. If inflation has been low, this means that value has been understood and appreciated in the social and political order. This would indicate that change is not going to be something over which the economy has to fluctuate. I think that the economic stability brought out in a situation where there is low inflation also reflects how individuals demonstrate a certain level of faith in both government and economy. One does not hear of steady economic progress in nations where there is a strong sense of dissatisfaction with political leadership. Obviously, when value is understood, then things are not all that bad- indicating that political leadership probably enjoys the support of the people. In the end, I think that low inflation is one of those benchmarks that can be used to reflect many other elements that are rooted in economics, but grow outside of it.
It does mean the things that the first answer mentions, but it means much more as well.
First, it means that the country has been relatively well managed. In countries where the government spends too much money (compared to the productivity of the country), inflation gets to be quite high. This is a major reason why many developing nations have had very high rates of inflation.
Second, it means that investors and people in general have a fair amount of confidence in the prospects for the country's economy. When people lose faith in a country's direction, inflation can often rise.
Both of these help to explain why places like Zimbabwe have had high inflation while more stable countries have not.
Mainly that production has kept pace with population.
The bumper-sticker explanation of inflation is too much money chasing too few goods. So:
If production stays constant, but population increases, there is scarcity, which leads to inflation.
If production increases, but population decreases, there is a surplus, which leads to deflation.
If production and population keep pace, but the money supply grows, there will be inflation. Whether or not it means anything is different question: eggs cost $2 per dozen now, far more than the cost in 1849. But would you trade the Internet, AC, and cell phones for all the gold at Sutter's Mill?
People generally dislike inflation irrespective of how low the rate of inflation may be. However, the economic development of a country is frequently accompanied with a positive rate of inflation. Also, in general all countries in the world have experienced a positive rate of inflation over more than 100 years. Thus we can say that some inflation is unavoidable. In a situation like this, a low rate of inflation for many years appears to be a good sign. However, correct assessment of the situation must also take in account the rate of economic development.