The words meat, meet, mete sound the same but have different meanings and spellings. Why do meat, meet, mete sound the same even though they are completely different words?
The answer is simple: meat, meet, mete are homophones of the English language.
The edible flesh of animals, especially that of mammals as opposed to that of fish or poultry.
The edible part, as of a piece of fruit or a nut.
The essence, substance, or gist: the meat of the editorial.
Slang Something that one enjoys or excels in; a forte: Tennis is his meat.
To come upon by chance or arrangement.
To be present at the arrival of: met the train.
To be introduced to.
To come into conjunction with; join: where the sea meets the sky.
A boundary line; a limit.
To distribute by or as if by measure; allot: mete out justice.
Archaic To measure.
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.