The Ambassadors can refer to two main things in this book: Strether's mission to persuade Chad Newsome to come home, and Strether's tendency to spend most of his time doing things for other people. In both cases, Strether needs to get a life of his own and start living it.
The image of an ambassador can also refer to the fact that Strether is a man with a mission in a foreign country who's trying to understand how people do things in Paris. The problem is that the more he understands it, the more he likes it and the more he neglects his job as Mrs. Newsome's ambassador.
Now you might say, "But why is ambassadors plural?" Well, Strether isn't the only ambassador Mrs. Newsome sends to Paris. Once Strether has switched sides and become a representative for Chad and Madame de Vionnet, Mrs. Newsome sends her daughter Sarah to check out what's going on in Paris. As Strether mentions at one point, "I feel like the outgoing ambassador […] doing honour to his appointed successor" (8.1.10), meaning that he feels like Mrs. Newsome has sent Sarah to Paris to replace him as the person responsible for bringing Chad home.
As with real-life ambassadors, people battle for power in this book by twisting language to suit their own ends. People reveal and conceal things for strategic reasons, and it seems that there is no sentence spoken in this book that doesn't have some sort of strategy to it.
But when you get a lot of egos coming together and trying to act like they're part of a polite society, you're going to get tons of little power moves that come out in language. In a way, everyone becomes an ambassador for their own interests.
Just think of the last time someone passive aggressively said to you, "Oh I just love how you'll wear anything." Yeah, kind of a jerk move. But it's tough to call them on it because they could totally accuse you of misinterpreting them. Then again, maybe that's just the Shmoop fashion police.