So "Meimei" is Taylor's widely-recognized Chinese nickname.
Pretty much every Western celebrity gets a Chinese nickname. For example, Katy Perry is "Fruit Sister," Benedict Cumberbatch is "Curly Blessing," and Taylor Swift is "Meimei" in China, with a literal meaning of, well, "Moldy" and "Unlucky."
An answer to why Taylor is nicknamed this way got about 7,000 supportors on Baidu Zhidao, a Quora-like Chinese site. Basically it goes that first, Taylor is very beautiful, and "beautiful" in Chinese is pronounced almost in the same way as "moldy" or "unlucky" — all are "mei," just with different intonations. Secondly, "every time Taylor debuted strong single aiming at crowning the Billboard Top 100 ranking, she bumped into different 'evildoers' and have to be stopped as a runner-up," so she's "Unlucky," but in a loving way.