I hear that it was a way to control people, or that was a way to make writing Chinese easier. What was the real reason?
Simplified Chinese had its roots long before the PRC was founded.
Soon after the Qing Dynasty was overthrown and the Republic of China founded, around 1920, scholars moved to create a new Chinese culture, one that is based on democracy and scientific methods like the western powers: the New Culture Movement.
Simplifying the Chinese writing is one of the suggestions. The scholars claimed that the Chinese writing was too complex, not suited to academic development and public education. It was taken up seriously by the ruling government because illiteracy was a severe problem in China.
In 1935, a first set of simplified characters with some 2,300 characters was published by scholars. The then Ministry of Education picked 324 characters out of the set and published the first official table of simplified characters.
Unfortunately, this policy came under heavy fire from the conservatists, and the Ministry withdrew it.
Then in 1949, the People's Republic of China was founded, and by 1950 they have started to collect the exiting simplifications people use daily. By 1956 they have passed the law to simplify Chinese writing. By 1964, the table of simplified characters have increased to 2,236. This went on to go through more adjustments and a finalized official table was published in 1986, now still in use.
In the mean time, the ROC government was defeated and retreated to Taiwan. With a total population of only about 7 million, and a significant portion being well-educated native Taiwanese (due to the Japanese investment in schools and public education), plus a powerful PRC just across the strait preparing to invade, the ROC government didn't feel the need nor had the time to keep working on simplifying the Chinese writing. Hence Taiwan kept on using the traditional characters.
It is important to note that Simplified Chinese arise out of a necessity which started very soon after the fall of the Qing Dynasty. It was not for political reasons.
It was part of literacy reform movement that started in mainland China even before the Communists took over.
Hong Kong and Taiwanese governments at the time weren't as focused on literacy efforts and simplified characters later became associated with the Communists.
Still, Singapore adopted simplified characters.