You use despite to introduce a fact which makes the other part of the sentence surprising.
in spite of
She has been under house arrest for most of the past decade, despite efforts by the United Nations to have her released.
她在过去10年的大部分时间里都被软禁,尽管联合国为解救她一直在做努力。
Despite being the world's richest nation, the USA is also one of the most religious.
尽管是世界上最富有的国家,美国也是最信宗教的国家之一。
You use despite to introduce an idea that appears to contradict your main statement, without suggesting that this idea is true or that you believe it.
She told friends she will stand by her husband, despite reports that he sent another woman love notes.
她告诉朋友们她将支持丈夫,尽管有报道说他给别的女人写过情书。