Is there a significant difference between "sobre" and "acerca de", when the intent is to describe the topic of something?
Where is "acerca de" a better choice than "sobre", and vice-versa?
They are exact synonyms (as RAE says), you can use any of them to replace the other because there's no difference in meaning or grammar.
sobre (RAE definition)
prep. Encima de.
prep. acerca de.
The word "sobre" can become, has the potential, to be a synonym of "acerca de"; when used as a preposition.
Although "sobre" can be used as a synonym; it is context dependent and can have multiple meanings. It is true that "acerca de" is a bit more precise, there is just one way of using it, only one meaning.
Examples of this ambiguity:
synonym of "acerca de"
El libro habla sobre la historia de Francia.
The book talks about the history of France.
locative preposition
Dejé el libro sobre la mesa.
I left the book over the table.
dominance, superiority
Estoy enojado por lo sucedido, pero sobre todo, por tu falta de respeto.
I am upset for what happened, but above all, for your lack of respect.
Those examples are for "sobre" used as a preposition, so it can be used on three different forms:
That is why it is context dependent.
Estimated reading time: 5 minutes.
No TL;DR, but the short answer is this:
If you never, ever used "acerca de" to mean "about," nobody would likely even notice. There isn't a context I've come across where you can't use "sobre" to mean "about" and with what might be one minor exception, it is far more frequently used to mean "about" than "acerca de" is. If you're a beginning student of Spanish and not quite ready to go more than one-word deep for each English word you know, stick with "sobre" when you want to say "about."
I actually wrote a post or article on this a while back for Duolingo, but my computer has been hacked since then and consequently I no longer have the notes on this topic I once did. The one thing I remember from it, though, is that I noticed the phrase "acerca de" seemed to be more frequently used with prepositional pronouns (e.g., mí, ti, ...).
In general, however, "sobre" looks as if it is used to mean "about" much more often than it is used to mean "over" (perhaps more than four times more likely) or "envelope" (perhaps more than 80 times more likely), using translations found at Reverso as an indicator. This probably explains why little confusion surfaces between meanings and context limits any confusion that might surface. Let's take this phrase as an example:
sobre el sobre
Standing alone like this, this phrase could mean "over the envelope" or "about the envelope," but when you give it more context, as in "La verdadera historia sobre el sobre equivocado en los Oscar," it is clear that the first "sobre" means "about" and the second "sobre" means "envelope." It is also very clear that the first "sobre" does not mean "over" (as in "on top of").
Givanse gave a very good answer and it was especially good because he mentioned that "sobre" can be used as a "locative preposition" or a "preposition of place":
Prepositions of Place tell us where things are, often though not always relative to other people, places and things. You will notice that the verb estar is often used (rather than ser) in these examples because it pertains to being and location.
— From "Prepositions of Place (Preposiciones de Lugar): How and When to Use Them," Wyzant
Even so, "sobre" appears to be more than four times more likely to be used as a word that means "about" than it is to be used as a locative preposition such as "over." If you do mean "over," however, "sobre" is a good choice. No other word is as closely associated with that meaning and it (or rather "encima de") is listed as the first meaning for "sobre" in the Diccionario de la lengua española (DLE).
Now, some of you might be thinking, Yeah, but wouldn't "about" be more common than "over" and "envelope" anyway, so isn't "acerca de" a better choice, because it's more specific? In fact, you mention this very thing. And I have to tell you that I like the way you think and try to practice using precise speech no matter what language I'm using. Furthermore, whoever thinks that "about" is more frequent than "over" and "envelope" would be correct. As an example I can't think of many reasons why Spanish would need to use any of these words — about, over, envelope — in more or less frequent ways than just about any other language, especially English, so let's take a look at what the distribution looks like for these three words in English:
In the Ngram above, "about" is one and a half times more frequent than "over" and more than a hundred times more frequent than "envelope."
I have to tell you that there's nothing wrong with using "acerca de" instead of "sobre" to mean "about” or “encima de” to mean “over." (Best word for "envelope," as in the kind you put a letter in, is going to be "sobre," so I won't use that as an example.)
And if you decided to use "acerca de" instead of "sobre," nobody is going to correct you if you're using it to mean "about" unless that person is simply asinine or contentious by nature or, for some other reason, wants to make a show of superiority over you by correcting you over something like this. One or the other may be more preferred by some, but one person's personal choice does not make the use of one word over the other "more correct" or even "better," so if you encounter someone who tells you that you need to use "acerca de" instead of "sobre," or vice versa, I would seriously question that person's credentials.
Givanse has already mentioned that
... "acerca de" is a bit more precise, there is just one way of using it, only one meaning
and it's true. But a lot of times, when students are learning a foreign language, they want to sound natural. They want to sound like a native. They want to use the same words and phrases those born and raised in a Spanish-speaking country do. And if that is the case for you, too, you'll want to use "sobre" for "about" most of the time, even if, technically speaking, the possibility for confusion exists.
Like I said earlier, the only exception to this that seems to be true is when "about" is followed by a prepositional pronoun, in which case, it looks as if "acerca de" might be about four times more common, if you go by online news articles. However, the context dictionary Reverso still shows "sobre" favored in such a construction by about 7:1. Bear in mind that the sample size I used to compare uses in online news articles was relatively small, but when I wrote an article on this a while back, I used a source other than Reverso and the use of "acerca de" with prepositional pronouns was significantly higher than with "sobre."
My main point to all of this is basically this: The word "sobre" means many different things, but just because a word can mean many different things does not mean that it does not also have closely associated meanings tied to specific words. To illustrate this point I'll end this by comparing a couple of words/phrases translated by Reverso:
"sobre" is used to translate "about" four times more often than "acerca de"
"sobre" is used to translate "over" 17 times more often than "encima (de)"