What does this mean?
 

When I started studying by heart the kanji (reading and meaning) I had found on the book I used that with ON reading you can have other kanji, while with KUN readings you will have hiragana.
Basically I knew that for roots of verbs you use the KUN reading and not the ON reading.

While making flashcards I encountered few exceptions and they all used the same hiragana. I don't remember all of them, but the ones I remember are: 点じる、転じる、生じる. What is that じる and does it have a special use with ON reading of kanji?

Those are all verbs in their plain or dictionary forms. that じる is the same as く in 行く or る in 来る.

Than I guess my book was wrong in saying that to form the root of verbs it is used the KUN reading of a kanji?

点（てん） in 点じる is an ON-YOMI reading. You can say the same thing about 転 in 転じる and 生（しょう） in 生じる. When you read a kanji with On-yomi reading, usually you don't put おくりがな after the kanji. This case is an exception. Almost all the verbs with じる or ずる after Kanji are very formal.

Hope it helps.

Hirashin

Thank you very much. I had just added more flashcards to my kanji list and found another one (同じる). It was getting a big coincidence about this じる...
Now I know that when I use them I am using a very formal verb, thank you very much.