For apps like Duolingo, the correct answer is the best translation, not necessary any correct equivalent translation. In this case, the authors of the app have decided that Beijing is a big place is most closely translated to 北京是个大地方. It's not bad, Beijing [北京] is [是] a [个] big [大] place [地方], but such clean and direct translations are uncommon.
The long structure is:
[noun] 是一个 [adjective] 的 [noun]
Where we have:
Běijīng shì yīgè dà de dìfāng
In this structure, we can replace the nouns and adjectives at will:
(Note we need to change the measure word accordingly.)
However, 北京是一个大的地方 (while grammatical) is rather long. Thus we...
Drop the 一个 (see Connecting nouns with "shi"). We can also replace 一个 with just 个 (see Measure word "ge"; Omitting the Number).
So we can say either of:
[noun] 是 [adjective] 的 [noun]
[noun] 是个 [adjective] 的 [noun]
In the case of 大的地方 we can drop the 的 (which we cannot do in general). In general, precisely when we can and cannot drop the 的 is tricky. As I understand, it is okay to drop the 的 in
大的[noun] (for one and two-hanzi nouns) and in most cases of single-hanzi adjectives (as in this case: 大). （There's likely exceptions to this.) Thus all of these are okay too:
As dan notes in the comments, in the case of 大地方 it's natural to think of this as a noun in its own right. In this case we're using the
[noun] 是一个 [noun] construct with 大地方 as the second noun. This is not generally true; something like 大机场 (big airport) would probably be interpreted simply as a short form of 大的机场.
(Side note: The most common case of dropping the 的 is to express closeness, e.g., 我妹妹, see Expressing close possession without "de", but it's not the only possibility.)
In total, that's six different grammatical ways of saying the same thing. So the app has chosen the one they consider most faithful to the English.
In response to What's the difference between adding and omitting a 个? If you include a solitary 个, it implies there's only one (of whatever your talking about). This is also mentioned in Measure word "ge"; Omitting the Number. However, there's obviously only one Beijing (so the distinction doesn't arise here). A case where it's relevant is 我们是好朋友 ("we are good friends"): you can't add a solitary 个 here because there's two people (not one), but you can say 我们是两个好朋友.
Finally, I feel it's more precise to say 城市 (chéng shì) = "city" instead of 地方 = "place". I also feel that 大 is an inadequate adjective to describe the "bigness" of Beijing. Thus I would say:
Běijīng shìgè fēicháng dà de chéngshì