"Sector" as an English translation for "secteur" is actually a bit of a false friend translation in this example. "Sector" in English in an economic context generally refers to a very large division of the economy - the private sector, for instance. The standard way to refer to fishing as an economic activity that is part of the economy is "the fishing industry." Here is a sentence taken from an English-language source (not translated), for instance: "The fishing industry includes any industry or activity concerned with taking, culturing, processing, preserving, storing, transporting, marketing or selling fish or fish products." And here is a recent headline from the New York Times: "Hawaii Lawmakers Press Fishing Industry." The preferred translation should definitely by "Fishing is an important industry" because that is the most natural way to express this idea in English. Just to be clear, I'm not suggesting that "sector" should necessarily be marked wrong, but rather that "industry" should be the preferred translation.
"...an important industry" makes a lot of sense but the word for "industry" (l'industrie) is not part of Duo's vocabulary. So someone thought that "secteur" would have to do. One could use this expression to refer to an economic segment of a country, thus, secteur agricole/bancaire/hospitalier = farming/banking/hospital sector. In everyday language, "le secteur de la pêche" would be called "the fishing industry" or alternatively, "the fishing/fisheries sector". Similarly, in this context, it could be understood as "Fishing is an important industry".