While most that is said there is correct, some comments exaggerate in the opposite sense, by downplaying the real higher quality of the Japanese swords in comparison with the contemporaneous swords of the 19th century (when most Westerners became aware of them).
Unlike what some say there, the fascination of Westerners for Japanese swords has not started after WWII. Already during the 19th century, the first Europeans and Americans who could visit Japan were all extremely impressed with the Japanese swords, as demonstrated in test cuts but also by cutting parts of human bodies in some incidents.
Even if in the more distant past there have been many places where swords of very high quality had been made, e.g. the Toledo swords or the Damascus swords, by the time of the 19th century such techniques had been forgotten for a long time and the remaining production of swords was oriented to the mass production of cheap but low quality swords. Such swords were more resistant to mishandling than the Japanese swords, but they could not compete in hardness and sharpness.
The same travellers who were impressed in Japan by the Japanese swords were not impressed at all by the swords encountered in the other countries of the region, e.g. by the Chinese swords.
At least by the time of the 19th century, in no other place were there smiths willing to spend so much time with the sharpening and polishing of extra hard steel.
Even today, when everybody knows modern metallurgy, using Japanese kitchen knives is a very different experience from using European kitchen knives (at least for me, one much more pleasant), due to the Japanese preference for maximum hardness and sharpness, despite the fact that such blades require much more care during use and maintenance.