Kanji were imported from China more than 1000 years ago. The Japanese incorporated both the original Chinese pronunciation (as they heard it) AND their native words for the similar meanings.
ON READING: Is the 'Chinese' Reading and is thus usually spelled in katakana
KUN READING: Is the 'Japanese' Reading and is written in hiragana.
For example: The Chinese (ON) reading for the character meaning 'tree' (木) is 'moku' but the native Japanese pronunciation is 'ki'
Usually, when you find two or more kanji glued together, you read them using the ON reading, but if if the kanji is by itself it usually has the KUN reading. 木曜日 (moku you bi) versus 木 (ki). That isn't a hard and fast rule, but it can allow you to make an educated guess!