The words idle, idol, idyll sound the same but have different meanings and spellings. Why do idle, idol, idyll sound the same even though they are completely different words?
The answer is simple: idle, idol, idyll are homophones of the English language.
Not employed or busy: idle carpenters. See Synonyms at inactive.
Avoiding work or employment; lazy: shiftless, idle youth. See Synonyms at lazy.
Not in use or operation: idle hands.
Lacking substance, value, or basis. See Synonyms at baseless, vain.
An image used as an object of worship.
A false god.
One that is adored, often blindly or excessively.
Something visible but without substance.
A short poem or prose piece depicting a rural or pastoral scene, usually in idealized terms.
A narrative poem treating an epic or romantic theme.
A scene or event of a simple and tranquil nature.
A carefree episode or experience: a summer idyll on the coast of France.
Definitions from The American Heritage® Dictionary of the English Language, 4th Edition and Wordnik.
Homophones (literally "same sound") are usually defined as words that share the same pronunciation, regardless of how they are spelled.
If they are spelled the same then they are also homographs (and homonyms); if they are spelled differently then they are also heterographs (literally "different writing").