Translation:Our cat is fat.
Actually, the use of "很" is due to the fact that the adjective is used predicatively. This can be seen in the fact that "很" is also used when the predicative adjective consists of more than one character: "我們的猫很漂亮."
In English, the use of the predicate adjective would be "(Noun) (be verb) (adjective)," but Chinese doesn't use "是" as the unmarked way to express predicative adjectives (Chinese can use "是" in these forms, but it tends to be more for emphasis/contrast, and with "的" used after the adjective e.g. " 我們的猫是胖的,一點都不瘦")
Also, note that when the adjective is used attributively (a noun phrase with an adjective modifying the noun), the adjective can be readily used without "很"--even if the adjective is only one character: "胖的猫最可愛."
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..."
Just in place of pang (no Chinese keyboard sorry)
I don't know the actual reasoning, but as a native speaker that forgot a lot of Chinese but just "knows" certain words' meanings as a result, you would use pang sort of describing something big because it's fat, whereas fei would be more describing something having fat. I could be wrong, but both are correct anyways.