"What is a 'study-bible' and how does it differ from a regular Bible?"
A study-bible is what the name implies; it is a Bible that is intended for study.
The way in which a study-bible differs from a regular Bible is that it is heavily annotated, generally by many dozens of individuals, most of which have a PhD and specialize in that given area of the Bible. Generally, a study-bible will have very lengthy introductions to all books of the bible and other relevant subsections of the text, occasionally have dedicated notes to a page, and will have a horizontal line separating the notes for each verse or section of verses from the text itself. Depending on the study-bible, the annotation can be anything from notes on the various translations of a tricky-to-translate bit of text, cultural allegories that would have been understood intuitively to the original readers of the text that are no longer understood, cross-references between one scriptural text to another, historic inaccuracies of the given text (I couldn't find it if you asked me to as it's written in a very large text and not accessible to search by technology, but some portion of the biblical book of Daniel has the incorrect historic succession of kings relative to various historic accounts and records we have for the time period. It's just an interesting note that would have entirely slipped over a person's head if they hadn't read that note.)
Subjective Thoughts and Experience
I own four study Bibles; the Cultural Backgrounds Study Bible, the New Interpreter's Study Bible, the HarperCollins Study Bible, and the Chronological Study Bible.
The HarperCollins Study Bible is likely the most reputable of the four given in that it has the largest group of contributors, dozens of PhDs. It, along with the New Interpreter's, contains the Apocrypha; which means you have the Latin Vulgate and the Orthodox books as well (such as Sirach, Maccabes, the books of Esdras, Judith, and so forth.)
The New Interpreter's is also very similar; it contains the books not in the Protestant canon. I can't remember how it differs from the HarperCollins, but it's another general-purpose one.
The Cultural Backgrounds one focuses almost solely on the cultures of the time as opposed to simply general notes or translation notes; how things would have been understood in the original Mesopotamian culture*, various cultural trends, norms, artifacts, historic texts outside of scripture, etcetera. It's my personal favorite, I take it with me almost everywhere I go.
I don't like the Chronological study-bible; which is a bit of an irony, considering it's the only one of the four that I have leatherbound with my name embossed on in silver on the cover. It's very clunky to navigate because it takes all the books and verses (which in any other bible are very ordered and organized, as well as consistent across translations) and arranges them all completely out of order. It also has a fair bit of ego; in the introduction to the text it claims that the Chronological Bible (itself) is the singular way the bible "ought to be read". I haven't bothered with it really. Maybe someday I'll pick it up and try to get myself to tolerate it, but for now I dislike it.
If you haven't already been able to derive this from the writeup thus far, I want to assert that I am of the opinion that any Christian person had really, really ought to pick up a study-bible. They bring comprehension of the text as well as awareness of inaccuracies and inadequacies of the text to a much, much higher level. I wouldn't even recommend reading any form of the Bible without notes or commentaries, but obviously that's preferable to not reading the Bible at all. Well, maybe. There's plenty of incorrect conclusions a person can come to if they read it without annotation.
* While the entirety of the Bible was not written with an ancient Mesopotamian worldview, a great deal of the "Old Testament" was reflective of the ancient near eastern cultures surrounding the writers, especially the parts written under the institution of first-temple judaism, the historic chronologies, arguably wisdom literature, and prophetic oracles. I am not saying that the entire Bible was written in Mesopotamia. I am simply saying that a great deal (or all) of the text is to some degree a product of its given culture.