This is something which will primarily of interest to those who are interested in Chinese script. During the heady days of the formation of the People’s Republic, various plans to encourage greater literacy were encouraged. Some had even seriously proposed getting rid of the Chinese script all together and replacing it with an alphabet, as was successfully done in Vietnam. However, another plan was eventually approved.
In Chinese, there long have existed simpler forms of some characters, often used in either cursive script or informal writing. In the first round of simplification, the Chinese government made these standard, both for printing and for handwriting. Later on, they reduced the number of strokes in others. Most Chinese characters also have a phonetic element. In some cases, with compound characters, they borrowed the phonetics with fewer strokes from other characters and thus created new characters. I’m not sure whether those who planned this were aware of this particular problem, but if you learn only the simplified characters and not the more complicated traditional set, it is more difficult to read things written in the traditional set. Taiwan, Hong Kong, and many other overseas Chinese communities, Singapore excepted, use the traditional set. (Singapore has four official languages, namely English, Malay, Chinese, and Tamil. For Chinese, the simplified set is official in Singapore.) It is easier for people trained in the traditional characters first to read simplified characters in addition to the traditional set they already know.
By order of the President of the Republic of China, the simplified characters no longer appear on Taiwan’s governmental websites. You can read more about this here. Taiwan is now welcoming more and more tourists from mainland China these days. However, even on governmental websites from Taiwan promoting tourism, mainland Chinese will no longer be able to access these sites in their simplified character versions. President Ma has previously asked UNESCO to register traditional characters as an intangible cultural heritage.
In Korea, the traditional set is official. However, I’ve noticed more and more simplified Chinese in Seoul and elsewhere.