stake 的本意是樁,支柱
have a stake in 的意思是,與 ...利害攸關
因此，
We have an enormous stake in each other's success.
意思是，壹直以來，兩國所取得的成功對雙方都有巨大的利害關系。
這段話我是這樣的：
At a time when some doubt the benefits of cooperation between the United States and China, this visit is also a chance to demonstrate a simple truth. We have an enormous stake in each other's success. In an interconnected world, in a global economy, nations -- including our own -- will be more prosperous and more secure when we work together.
曾經有人對我們中美雙方的合作利益產生質疑，而這次訪問又給了我們壹次機會來證實這壹簡單的真理。壹直以來，兩國所取得的成功對雙方都有巨大的利害關系。因此，我們的合作必定會讓這個相互依存的世界和全球經濟國（包括中國和美國）更為繁榮昌盛，社會更加安定。