There are several books available on various Agile methods, e.g.:
I can also recommend Alistair Cockburn's Agile Software Development, which gives a general overview of the topic, the philosophy behind the Agile movement, and briefly introduces various concrete methodologies.
What else can I read to get a reasonably comprehensive overview of what people (and by people, I mean people writing job adverts) specifically mean when they talk about Agile Software Development?
I would venture to say the typical HR guy/gal doesn't understand much of all this, they just know Agile is a buzzword in fashion, so they apply pattern-matching to the text of CVs received ;-)
I get the sense that there are a few people using the term pretty loosely
Only a few? ;-) Jokes aside, since Agile became fashionable, inevitably crowds of people started to talk about it without any actual experience of it. It is unfortunately very typical that managers brag about their SDLC being agile this and agile that, while in fact it is still some overcontrolled heavyweight big-M Methodology - or its opposite, cowboy coding on the loose.
So don't be too impressed by people talking about Agile - check whether they have any actual first-hand experience in it before believing what they say. Whenever someone tells you "oh, we use Scrum / XP / ... in our project", ask them about the details. Do they implement the process by the book, or have they modified it to suit their needs? Modification and adaptation of the SDLC is completely OK and in fact, part of any healthy agile process - up to a certain limit. But if a team claims to use e.g. XP, "only the customer is not sitting with us, we communicate via email... and we don't do pair programming because management disapproves it... oh and we don't have unit tests and continuous integration... and we document the requirements using a standard 50-page Word template... but other than these, we are fully Agile!"... well, then they aren't doing XP.