Cyrillisation in the Soviet Union is when the big people in charge decided that everyone should write and read things in a special way. This special way was called the Cyrillic alphabet, and it used different letters than the alphabet that you and I use.
Now, you might be wondering why they wanted everyone to use this new alphabet. Well, the big people in charge thought that it was important for everyone to be able to read and write in the same way. That way, people from different places in the country could all understand each other, even if they used different languages.
So, the big people in charge made a rule that everyone had to start using the Cyrillic alphabet. They printed new books and newspapers in this alphabet, and they made schools teach kids how to use it.
Some people didn't like this change at first, because it was hard to learn a new way of reading and writing. But eventually, everyone got used to it, and now most people in Russia and other countries that used to be part of the Soviet Union use the Cyrillic alphabet just like you and I use the alphabet we know.