Learn Turkish: Lütfen burada durun.

This is due to 4-way vowel harmony. The root of the verb is dur- (to stop). Because the vowel in the root is u, the imperative suffix -In adapts to become -un.

Does durun mean I am telling multiple people to stop, or just one person politely?

It could be either! In Turkish, the plural form of "you" (siz) is also used to be polite or formal to a single person. Combined with lütfen (please), this is very likely a polite request to one person (like a taxi driver), but it could just as easily be addressed to a group.

The lesson also mentions the ending -InIz. Could I say Lütfen burada durunuz?

Yes, you can. Durunuz is an even more formal, official version of durun. However, in everyday spoken Turkish—like asking a driver to pull over—durun is much more common and still perfectly polite.

Why is it burada instead of just bura?

Bura means "this place" as a noun. To say "at this place" or "in this place" (which translates to "here" in English), you need to add the locative case suffix -da / -de. So, bura + -da gives us burada.