When you need to spell your name or address
Listeners may have difficulty understanding the letters because so many sound alike - bee, cee, dee, gee, etc. It is common practice to say an ordinary word beginning with each letter. For example, I might say, "My name is Joan. That's J as in July, o as in office, a as in apple, n as in Nancy." The Federal Aviation Authority (FAA) pubishes a list of good words to use, especially in international aviation, because they are not easily confused even by speakers and listeners using English as a second language.
The pronunciations given here tend toward the British variety of English, for example, dropping the final "R" of Oscar and Victor. Most Americans pronounce final R. But the words are unambiguous with either pronunciation.
The choice of words has a rather dated flavor, coming from military pilots' radio communications (uniform, victor, alpha, charlie, delta - Greek letters have been used to name companies in the army), from elegant parties with dancing (foxtrot, tango) and drinking (whiskey) at fancy resorts (hotel, golf); from geography (Lima, India, Quebec, Sierra, Yankee, Zulu); from people's names (Charlie, Juliett, Mike, Oscar, Papa, Romeo, Victor). And then the miscellaneous remainder (bravo, echo, kilo, xray).
The numbers are distorted in this system to make each one more distinctive and to avoid consonants that are difficult for second-language speakers. "Tree" avoids the challenge of the "th" in "three"; "fife" avoids the "v" sound. The two syllables of "sev-en" make it distinctive however distorted the "v" sound may be. Making "nine" into a two-syllable word distinguishes it from the long i sound of "fife". The rationale behind "fow-er" may be to distinguish it from the monosyllable "fife", both beginning with "f".
So when the air traffic controller tells your pilot to land on Bravo runway and proceed to gate Hotel Wun Tree, you can be fairly sure your pilot will understand!