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Dictionary definitions for the English language usually have the word spelled out in Greek letters to indicate how the word is pronounced phonetically.

Examples highlighted:

What are these Greek phonetic words called? And more importantly, where is it writ how these should be pronounced? I find them unhelpful because of my ignorance and I'd like to learn.

It's not "Greek". It's the IPA - International Phonetic Alphabet.

The International Phonetic Alphabet (unofficially—though commonly—abbreviated IPA) is an alphabetic system of phonetic notation based primarily on the Latin alphabet. It was devised by the International Phonetic Association as a standardized representation of the sounds of oral language. The IPA is used by lexicographers, foreign language students and teachers, linguists, speech-language pathologists, singers, actors, constructed language creators, and translators.

The IPA is designed to represent only those qualities of speech that are part of oral language: phones, phonemes, intonation, and the separation of words and syllables.To represent additional qualities of speech, such as tooth gnashing, lisping, and sounds made with a cleft palate, an extended set of symbols called the Extensions to the International Phonetic Alphabet may be used.

There's a chart with the sounds the symbols make on the IPA's official website.

It's not completely true that it is not Greek. Yes, it is IPA, but they needed so many symbols for IPA that they borrowed from Greek for some of them.

Many of them,

⟨ɑ⟩, ⟨ꞵ⟩, ⟨ɣ⟩, ⟨ɛ⟩, ⟨ɸ⟩, ⟨ꭓ⟩, and ⟨ʋ⟩

have different Unicode characters, but are Greek for practical purposes,

⟨θ⟩

is a actual Greek Unicode character, and

⟨β⟩ and ⟨χ⟩

are usually represented by the actual Greek letters though they are not supposed to be.

This is described in Wikipedia.

Some of the modified letters look as close to Greek letters as to Roman ones:

⟨ʋ⟩ ⟨ʙ⟩, ⟨z⟩, ⟨ⱱ⟩, ⟨ɵ⟩, ⟨ɛ⟩, ⟨ɜ⟩, ⟨ɤ⟩, ⟨ʏ⟩, ⟨ʊ⟩, ⟨ɪ⟩, ⟨o⟩, ⟨ʌ⟩

So, taken all together, and from the point of view of someone familiar only with the Roman and Greek alphabets, it does appear to have a significant proportion of Greek in it.