I'm working with the CMU pronunciation dictionary and I can't comfortably say I can understand what difference in sound they're trying to indicate by splitting AA and AO into different phonemes.
Wikipedia gives "balm" and "bot" as examples of the AA sound and "bought" as an example of the "AO" sound, but I don't detect a difference in vowel sound when I say the three words.
I also went through the CMU dictionary to look for examples of AA and AO words and still can't figure it out.
Words like bot and bought originally had different vowel sounds, but for some North American speakers, these vowels are now merged to a single vowel phoneme. This merger is called the "cot-caught merger"; there is a previous question about it: Why are many TV personalities beginning to pronounce "daughter" as "dotter"?
For speakers with or without the merger, there are a variety of ways that these vowels can be realized phonetically. The vowel in bot (symbolized in the CMU pronunciation dictionary as AA) is most commonly transcribed in the International Phonetic Alphabet as [ɑ], but speakers with the "Northern Cities Vowel Shift" use a quality more like IPA [ä] instead. The vowel in bought (symbolized in the CMU pronunciation dictionary as AO) is most commonly transcribed in IPA as [ɔ], but some speakers use a quality closer to [ɒ], and the linked Wikipedia article says that speakers who pronounce bot with [ä] may pronounce bought with [ɑ].
The remarks in the previous paragraph apply to North American English specifically. Outside of North America, bot and bought are generally pronounced with two different back rounded vowels, the second distinguished from the first by a combination of greater length and greater closeness (a.k.a. greater vowel "height"). So a common convention for transcribing an "R.P." English accent is [ɒ] for bot and [ɔː] for bought; an alternative transcription that might better represent the usual modern values in England would be [ɔ] for bot and [oː] for bought.
You seem to be an American English speaker with the cot-caught merger. In that case, there isn't really a single vowel in your accent that is exactly equivalent to the "AO" phoneme, because as explained above, the AO phoneme has different phonetic values in different accents. The vowel that you use in words like orange and port might be similar, but that is not certain. The reason the CMU dictionary transcribes orange and port with "AO" is because some American English speakers with a distinction between the vowels in bot and bought find that their pronunciations of bought, orange, and port sound like they contain the same vowel phoneme. However, this isn't the case for all speakers of American English. Some speakers instead pronounce orange with the same vowel as bot or tar. Other speakers find that orange is best described as containing an allophone of the "long o" phoneme found in words like goat. (For example, tchrist, a fellow member of this site who distinguishes an /ɑ/ phoneme from an /ɔ/ phoneme, has stated that he finds the vowel in words like Tory seems to have neither of these two phonemes, but instead the third phoneme /o/).
Ok after continuing to go through the CMU dictionary I found some examples that made sense to me:
"AO" is the sound in "orange" and "port" where you bring your tongue and mouth in tighter than when you make the "AA" sound.
