Translation:Our cat is very fat.
I think the "hen" here helps the adjective to be two characters, so you can say "very fat," or "fat," and both should be acceptable.
I am pretty sure you are like me, a Chinese from the Diaspora who has always been taught that 很 means "very". I upvoted you because I see that you have -1.
But just note that Duo is teaching a very specific brand (dialect?) of Mandarin. I am learning new things too.
Thanks for upvoting LilyYang's question. I think some people do that as a quick way to "answer" no to someone's question. But the system will hide a post with -3 or lower votes and then others who could learn from it might not see a perfectly valid question. I'll down vote a post with bad information or if the same question has already been ask and answered lots of times, but this is a good question that deserves an answer even if the answer is "No, because..."
I think some people downvote comments if they see that the same question has been asked and answered a hundred times before. Every time 很 is used in a sentence, there's at least one comment asking why there is no "very" in the translation
Our Chinese teacher from Beijing said he would rather use 肥(féi) about animals
I think the 很 here is just the mandatory qualifier, which doesn't actually qualify the state or verb. It's just there because the grammar demands it.
非常胖 would be "very/extremely fat", I think.