The meaning isn't different, but the grammar is slightly incorrect if you use "than" in this way. To write the sentence with "than," you would also need to add the word "more" (so you would say "holding three times more carbon than the entire atmosphere"). It doesn't quite make sense to say "three times than" -- you have to say "three times more than." To use "as," a slightly more elegant construction would be to say "holding three times as much carbon as the entire atmosphere." Your version with "as" is also perfectly clear, but doesn't sound quite as natural. There's no difference in meaning between "three times as much as" and "three times more than," but I think the second option sounds more emphatic, since it emphasizes that there is a lot *more.*

Hi! You use "as" when you want to tell something that is the same. "A car has the same amount of wheels as a bus" You use "than" when you want to tell something that is not the same. "A car has more wheels than a bike" Hope this helps?