It is true that strictly speaking, both "um" and "und" make sense here on a grammatical level. The reason why "um" has to be chosen is because the variant with "und" does sound rather weird.
As various other posters seem to think "und" would be ungrammatical here, let's expand the relevant parts of the sentence a bit:
Die Einrichtung von sogenannten Biosphärenreservaten in Deutschland wurde durch die UNESCO angeregt, u(m) Regionen zu kennzeichnen
We need only this part. Anything that follows afterward further specifies which regions we are talking about, which is irrelevant for the sentence structure at this point.
If we insert "und" in the above sentence, at first glance, the part after "und" is not a complete sentence: "Regionen zu kennzeichnen"
However, this in itself is not sufficient to discard "und": Incomplete sentences frequently indicate that there is some ellipsis at work, usually of a part of the sentence that would otherwise appear twice. A simple example would be:
Ich gehe Brot kaufen und Fische angeln.
"Fische angeln" certainly isn't a complete sentence, but it becomes one by connecting it to the - mutually used - first part of the sentence:
Ich gehe Brot kaufen
und
ich gehe Fische angeln.
Now, word ordering in the two partial sentences can be varied independently:
Brot gehe ich kaufen und Fische angeln.
This is still correct - but note that I perceive this as a slightly stilted and/or old-fashioned way of putting the statement.
However, the above sentence could be interpreted to work the same way. From that viewpoint,
Durch die UNESCO wurde die Einrichtung von sogenannten Biosphärenreservaten in Deutschland angeregt und Regionen zu kennzeichnen.
could be expanded to
Durch die UNESCO wurde die Einrichtung von sogenannten Biosphärenreservaten in Deutschland angeregt
und
durch die UNESCO wurde angeregt, Regionen zu kennzeichnen.
Now, while I think such an ellipsis is grammatically valid, we see that the structures of the two sentence parts do not match as nicely as in the above example. The fact that one occurrence of "angeregt" goes with a noun phrase (which, in the sentence as given, is placed before "angeregt") and the other one with a "zu"-infinitive verb phrase (which is placed after "angeregt") makes the sentence with the ellipsis sound awkward, like badly written text.
This is why "um" is the more likely choice here - while both "und" and "um" would make sense grammatically, only "um" does not make the sentence sound off.
The other reason why "um" is to be preferred is that it makes more sense semantically - the described "Einrichtung von Biosphärenreservaten" and the "Kennzeichnen von Regionen" are not two separate events, but the latter is the objective of the former. Therefore, establishing the intention with "um" is a reasonable assumption.