ON-YOMI (音読み) readings are those which were derived from classical Chinese pronounciations and in most cases, are used for compound words – eg 食事 (shokuji) – which are formed using multiple Kanji characters, similar to how Latin and Greek roots are used in compound words in European languages.
KUN-YOMI (訓読み) readings are native Japanese readings and are used in most cases when you see a Kanji character on its own – eg 白 (shiro) – and in all cases where you see Okurigana (ending with Hiragana) – eg 食べる (taberu).