The term "ambivert" was popularized by Dan Pink in 2013, in an article on leaders and sales. The word operates in the same colloquial universe of definitions in which introverts are shy and retiring and extroverts (usually spelled with an o) are loud and outgoing.
Here's an excerpt from Pink's article in the Washington Post:
So what kind of personality makes the best salesperson — and therefore, presumably, the most effective leader?
Most of us would say extroverts. These wonderfully gregarious folks, we like to think, have the right stuff for the role. They’re at ease in social settings. They know how to strike up conversations. They don’t shrink from making requests. ...
The conventional view that extroverts make the finest salespeople is so accepted that we’ve overlooked one teensy flaw: There’s almost no evidence it’s actually true. ...
Does this mean instead that introverts, the soft-spoken souls more at home in a study carrel than on a sales call, are more effective? Not at all.
The problem with these paragraphs (and with the entire article), is that extraverts are not, necessarily, "wonderfully gregarious folks..." and introverts are not (again, necessarily) "soft-spoken souls more at home in a study carrel".
The problem with the article is that Pink is using the common misunderstandings of introversion and extraversion.