What are the 'kun' and 'on' readings of kanji?

おんよみ is the Chinese reading of a kanji and くんよみ is the Japanese reading. On-reading is usually used when the kanji is a part of a compound (two or more kanji characters are placed side by site). Kun-reading is used when the kanji is used on its own, either as a complete noun or as adjective stems and verb stems.

For example the kanji for water = 水。The On-reading for the character is "sui" and the Kun-reading is "mizu." "水　(mizu)" is a word in its own right, meaning "water". The kanji compound "水曜日(Wednesday)" is read as "suiyoubi."