Codex (COH-decks), plural codices (CAW-diss-eez). The modern form of the book, in which pages are folded down the middle and then sewn or glued in place; the whole thing can then be protected with a hard cover of some sort.
Life Before Codices
Ever since the Second Temple period, which is to say beginning in roughly the sixth century B.C.E., educated Jews used scrolls as a medium for their sacred books. To this day, the copy of the Torah that is housed in a synagogue is always a handwritten scroll, never a "book" in the sense that most people in Western culture think of books.
Scrolls were generally made of parchment (prepared animal hide) or papyrus (the dried leaves of an Egyptian marsh plant) and glued together into a single band. The longest scrolls measured between thirty and thirty-five feet (ten metres, give or take). A scroll of this length could comfortably contain roughly 18,000 words, depending of course on the scribe's handwriting, the size of the margins, and the language he used; longer works would be divided into separate "books" (think of the volumes of an encyclopaedia). The scribe would write the text in parallel columns on one side of the material only, then he would wind the whole thing around a pair of wooden rods. The reader, then, would twist the rods as she read, "rewinding" when she was done.
Scrolls were particularly popular among Jews, but for a long time, Greek and Roman authors favoured them too. Ancient libraries would keep their volumes (Latin volumen, "rolled up") in jars, or in pigeonholes in the wall, rather than on the shelves that we are used to.
But Then the Christians Came Along
However, sometime around the second century C.E., a new kind of bookmaking became popular. The types of books that were produced during this time period would be much more familiar to the modern eye: the pages are folded and bound, then placed between hard covers, just like that novel you bought at the bookstore last week.
One of the immediate advantages of this form was that both sides of the writing material could be used. The creation of quality parchment and papyrus was an expensive and labour-intensive process, so anything that saved resources was valuable.
Perhaps for this reason alone, the codex would eventually have become the dominant form of creating and reproducing texts. However, the rise of Christianity in the ancient Mediterranean vastly accelerated the production of codices.
Christians believed that the prophecies in Jewish scripture referred to the events of Jesus' life. To make their case, they would proof-text -- in other words, they would find a passage in an ancient prophecy and then explain how it predicted something about Jesus. For an example of how this is done, read Matthew 2:16-18, where a recent event is described and then linked back to an Old Testament prophecy. Matthew loves doing this: there are at least fifteen such fulfillment citations in his gospel.
This reading strategy meant that Christians were expected to jump back and forth frequently between related texts. All this rolling and unrolling of scrolls became very cumbersome. It was much easier to flip pages than to wind and unwind scrolls, which meant that the codex swiftly became a popular form for Christian books. Moreover, scrolls were not long enough to contain the growing corpus of Christian material; a single gospel will fill a scroll (and in the case of long gospels like Luke, it's a tight fit). However, multiple gospels -- such as, say, four -- could fit nicely into a single codex. So could the collected letters of Paul. And so on.
As I said, perhaps the change from scroll to codex was inevitable; codices were cheaper and more convenient for everyone, not just Christians. However, enough books from the first few centuries of this era survive to demonstrate that Christians very quickly latched onto the codex as a medium, while pagans and Jews made the shift more reluctantly. Once the Roman Empire became Christianized, the codex form gained even more popularity and eventually became the standard.
Arguably that is still the case today, though occasionally you will hear people making the claim that the printed book is soon to die out and be replaced by CDs or something even more ephemeral.
Further Information
Arthur Patzia's The Making of the New Testament has an excellent chapter on scrolls and codices, including interesting charts and statistics comparing the use of parchment and papyrus, and the numbers of pagan books versus Christian books, over time.