Kanji script is of Chinese origin. The Japanese incorporated a Japanese reading along with the original Chinese reading.
On-reading (On-yomi) is the Chinese reading of a kanji character. Chinese also used it that way at that time. But it might be quite different from Standard Mandarin today. The Kun-reading (Kun-yomi) is the native Japanese reading.
Even though which reading is to be used depends on specific words, as a general rule On-reading is usually used when the kanji is a part of a compound (two or more kanji characters are placed side by side). Kun-reading is used when the kanji is used on its own, either as a complete noun (word) or as adjective stems and verb stems. This is not a hard rule, but it would help to start with till one recognizes the usage and learns the pronunciation of the word.
Kanji Alphabet (One pronunciation)
S.No. On-reading Kun- reading Meaning Link
1. Ichi hito One, Unity http://japanese.about.com/library/blkod1.htm
2. u, yuu migi right, right wing http://japanese.about.com/library/blkod2.htm
3. u, ame, ama rain, rainfall http://japanese.about.com/library/blkod3.htm
4. en maru circle, yen http://japanese.about.com/library/blkod4.htm
5. ou no reading king http://japanese.about.com/library/blkod5.htm