Translation:There are a lot of people.
What's the difference between, おおぜいの人がいます and 人がおおぜいいます?
Edit: Yeah this is definitely a particular case. I think I understand what's happening now, though; thanks for the feedback guys & thanks for the links, powelliptic. So what it seems is that the first sentence uses おおぜい as a の-adjective, whereas the second uses it as an adverbial-noun. Both mean roughly the same thing. See: https://jisho.org/search/%E5%A4%A7%E5%8B%A2%20%23sentences for examples. Incidentally, only a subset of Japanese words can be used as adverbial-nouns.
On Jisho.org, 大勢 (おおぜい) is listed as, "Noun, の-adjective", but also as an "adverbial noun". If you look up "が大勢います" in quotes, there's a fair amount of Japanese-based sources that use that form. According to, https://www.kanshudo.com/grammar/adverbial_nouns, "An adverbial noun is a noun used to modify a verb directly. Approximately 700 Japanese nouns can be used in this way...No particle is needed to use the noun adverbially in this way."
I don't think you could have that second sentence - it would have to be おおぜいの人がいます and 人がおおぜいです. The difference is that in the first sentence the adjective is directly modifying the noun (with the help of の) whereas the second sentence is a simple A = B type sentence. It's a little easier to see the difference with another adjective and noun for comparison - for instance, if the adjective was red and the noun was car 赤い車があります - there is a red car or I have a red car, and 車は赤いです - the car is red. It's harder to make the distinction clear in your English translation for the original sentence and your second sentence - I'm not sure how you could make the difference clear.
I can't speak to the difference between the two, but I must disagree with the other answers and say I think they are both valid. I've seen 大勢+verb in the wild, and Wiktionary says 大勢 is an adjective as well as a noun:
Duo itself uses the latter structure in its prescribed answer for another question ("There are a lot of men." = "男の人が大勢います。", https://forum.duolingo.com/comment/23045592).
No, because unlike Japanese, English verbs (sometimes the endings and sometimes the whole verb) change to show person - there is, there are etc depending whether it is first person singular (I), second person singular (you), third person singular (s/he/it), first person plural (we) etc.
Colloquially it depends on the word immediately following. In a proper essay, one would say "there are many" rather than "there's a lot" simply because "many" is a slightly more formal word than "a lot" - however, in common speech, both "there is a lot" and "there are a lot" are interchangeable.