Symbolism, Imagery, Allegory
As the title might suggest, the symbol of the ambassador is central to this story. And the reason it's so important is that this book is, among other things, really interested in language, communication, and most importantly, manipulation.
The first mention we get of this title metaphor is in the second sentence of Book 4, Chapter 2, where James writes, "It really looked true moreover from the way Chad was to behave after this. He was full of attentions to his mother's ambassador" (4.2.1). The sentence identifies Strether as Mrs. Newsome's ambassador, which has the effect of telling us that Strether isn't really his own person, but more like a servant to Chad's mom. Yeah, it's pretty sad.
Like a real-life ambassador, Strether learns very quickly that there's a lot of power in language and in speaking, especially if you can make words reveal and conceal whatever information is actually important. For example, he spends the entire first part of this book trying to figure out if Chad Newsome's relationship with Madame de Vionnet is sexual. But everyone he meets seems to be extremely skilled at dancing around the truth.
Further, Strether notices the importance of language when he goes to a party and see an actual (non-symbolic) ambassador talking to Madame de Vionnet: "His French has quickly turned to equal English, and it occurred to Strether that he might well be one of the ambassadors" (5.2.8). This ambassador's agility with languages symbolizes just how important your language skills are for representing the world in the exact way you want to mold it.