Tripartite means 'having three parts' or 'involving three sides'. It is a formal word, and you meet it in two situations. First, in talk about agreements and organisations: a tripartite agreement is one signed by three governments, three companies, or — very commonly — by workers, employers and the government together. Second, in description of how something is built or divided: a tripartite structure is one that falls into three sections, which is how a writer or an art historian might describe a painting, an essay, or a system. Notice the difference from 'triple': triple usually means three times as much of the same thing, while tripartite means one thing made of three distinct parts, and each part is usually different from the others. This is not a speaking word. In conversation people just say 'three-way' or 'three-part'. Save 'tripartite' for reports, contracts, and academic writing — and don't be surprised that it is much more common in the newspaper than in anyone's mouth.