This is an interesting question! We most often say “dream about” when talking about a dream you have while sleeping. For example, “last night I had a dream about school.” This usage is more mundane. On the other hand, “dream of” is more poetic. You hear it more often in songs, literature, speeches, and so on. If you’d like more examples, I’m happy to provide some.

Mara’s answer was great. Dream of is usually used to talk about ambition, or a desire or want. I dream of visiting Australia, I dream of having more students to teach etc. And dream of (often used in past simple) is usually about things we’ve dreamt about, either literally while asleep or figuratively. Last night I dreamt I was being chased by a ghost, I dreamt about succeeding in life etc.

The answer to your question is not specific to dreaming, but applies as well to "to speak of" and "to speak about" "to read of" and "to read about" "to think of" and "to think about" "Of" and "about" are very different sorts of prepositions. "About" establishes a relative LOCATION. "About" also has uses unrelated to location but those are always metaphoric and the source those metaphors is always location. Here are some location pronouns used in sentences: The cat is ON the table. The cat is UNDER the table. The cat is ABOVE the table. The cat is OVER the table. The cat is BY the table. The cat is ABOUT the table. The last sentence means the cat is somewhere near the table. If the cat is "about" the table, it could be on, under, above, over, or by the table. It means the cat is located in the immediate vicinity of the table. If you "dream about Charlie", it means that Charlie is the location (figuratively speaking) of your dream. The connection between your dream and Charlie is a strong one. Charlie is what your dream was ABOUT! "Of" is about relationship, not location. That relationship can be ANYTHING. It need not have much significance. If you think or dream OF Charlie, it only means that there is some connection, maybe a vague one, between your dream and Charlie. Charlie may have appeared in your dream but played no important role. "Dreaming of Charlie" does not mean that Charlie did not play an important role in your dream. Charlie could have been important in the dream. The dream may have been ABOUT Charlie. You can dream "of" and "about" Charlie at the same time. "Of" is not specific - it refers to any connection whatsoever. Every dream about Charlie is also a dream of Charlie, but not every dream of Charlie is a dream about Charlie. Hope that helps.