Q. What is On-reading and Kun-reading?
A. Kanji was imported from China around the 5th century. The Japanese incorporated both the original Chinese reading and their native Japanese reading.
On-reading (On-yomi) is the Chinese reading of a kanji character. It is based on the sound of the kanji character as pronounced by the Chinese at the time the character was introduced, and also from the area it was imported. That is why the On-reading might be quite different from Standard Mandarin today. The Kun-reading (Kun-yomi) is the native Japanese reading associated with the meaning of a kanji. Here are some examples.
Almost all kanji have On-readings except for most of the kanji that were developed in Japan (e.g. 込 has only Kun-readings). Some dozen kanji don't have Kun-readings, but most kanji have multiple readings.
Vol. 44: How do you know when to use On-reading and Kun-reading?