No matter where you live in the world, there is sort of a minimum value that your currency needs to practically be able to represent somehow. If your standard unit of currency is more than that minimum value, you need to subdivide your currency to be able to represent smaller values. In the U.S., we subdivide our U.S. Dollar into 100 cents, meaning that the smallest value that you can spend is $0.01. (My parents talk about being able to go to the store when they were kids and buy candy for 1 cent, but that is no longer the case.)
If your standard unit of currency is small enough, you don't need to subdivide it any further. This is the case with Japanese yen; 1 yen is roughly equivalent in value to 1 U.S. cent, and you won't find anything for sale in Japan for a fraction of a yen.
I visited the Czech Republic last summer. One Czech koruna is roughly equal to 4 U.S. cents, and I didn't see anything for sale there for fractions of a koruna.
There really isn't anything more to it than that. If we, in the U.S., decided that we didn't like the decimal point anymore and valued everything in cents, nothing would change, except that what we know today as the one-dollar bill would have the number 100 on it, and a price tag that had $4.95 on it today would look like 495¢ instead.
Currencies change in value with respect to each other from time to time. You can read about some of the events in the past that affected the value of the Japanese yen on the yen Wikipedia article, but none of that history is really relevant if you are concerned about the value today. If a currency goes up in value, it will just have to be subdivided more so that the smallest values can still be represented. If on the other hand, the value of the currency goes down (much more common), some of the smallest subdivisions will be eliminated. Canada has already stopped production of their penny, and there is discussion in the U.S. about doing the same here.
When the Euro was created (about 20 years ago), they had to pick some value to begin with, and they chose to make the Euro equal in value to the U.S. dollar at the time. It has since changed in value with respect to the dollar, and today 1 euro = $1.11 USD.