What is an enchanted book?
According to the Minecraft Wiki, an enchanted book is an item which allows players to add enchantments to weapons, tools, or armor by combining the enchantment book with one of said items on an anvil.
Can they receive any enchantment?
Testing in creative and survival mode shows that books can receive any enchantment that a normal weapon/armor/tool/other can receive. An easy way to check is to go into creative mode and use the new search function to search for the term book. This will show you what all the enchanted books are.
Can they receive more than one enchantment?
According to the wiki, books may only have one enchantment. This can be tested by giving yourself a bunch of books and enchanting them, then throwing them into lava or whatever you wish to do with them.
Since enchantments have different chances of occurring for different tools, materials, and at different levels, how are those probabilities different for books?
This would be different for books since books are not diamond swords. However, this would have that many variables because unlike a sword, books can only be made from paper. Swords can be made from diamonds, iron, and other materials. You would have to test this to truly know, but if John tells us how many levels he invested into his enchanted books, we might be able to know. Right now, though, it appears that the enchantment gives you the highest level (ex. Protection IV, Sharpness IV, etc.)
You can use commands to create items with any enchantments:
/give @p iron_sword 1 0 {ench:[{id:16,lvl:10}]}
There is no other way in vanilla. Someone else might know a mod that does that, though.
Best Answer
The book is for enchanting items on the anvil.
To make an anvil you need 31 iron ingots. In a crafting table grid, place 3 blocks of iron across the top, 3 iron ingots across the bottom, and an iron ingot in the center:
Then place the anvil, use it, place an item in the first slot, the book in the other. The enchantment costs Experience levels too (and you gain these gathering experience spheres by killing monsters, mining minerals, and smelting items.)
For example, a book of Sharpness III used on iron sword will make the sword cause 1.5 heart more damage on each hit.
You can enchant normal books too, using enchanting table - which might seem useless since the resulting book will have only one enchantment and you'll have to pay the exp cost twice (first, creating the book, and then again, enchanting the item with the book on the anvil). The serious advantage though is that the enchanting table gives enchantments randomly while the book gives the item exactly the enchantment of the book.
Imagine you want to make your diamond boots to have featherfalling enchantment. You can waste 40 diamonds on enchanting one pair of boots after another on the altar until you finally get the featherfalling - or you can use up a bunch of leather and paper until you get a book of featherfalling, then just apply it to a single pair of boots - 4 diamonds total.