The Wikipedia entry is actually flawed, which surprises me. In computer programming and data structure design, a "B-tree" is a "binary tree." It is called this because each node can have at most two nodes connected to it.
B-trees are data structures used in many, many places in computer programming, not just disk directories. A type of parser used in writing compilers called a "recursive descent parser" takes a computer program written in a high-level language, generates a "parse tree" that is a B-tree, and then emits object code as it walks the tree. A program I once wrote that plays the game Othello makes a B-tree of all the possible moves, then walks the tree looking for the best move. Compression programs that use a type of compression called Huffman encoding work by generating a B-tree of the data to be compressed. Some sophisticated sort algorithms construct a B-tree of the information to be sorted.
Edited to add: It is important to understand that the Attribute B-Tree in a Mac disk directory is not the same as the catalog B-tree.
The catalog B-tree is a binary tree that keeps track of all the files and folders on your disk. It also makes use of another data structure, the Extents B-tree, which is a binary tree that keeps track of files that are broken up in multiple pieces on a disk. f either of these things is damaged or corrupt, you're in trouble--you may lose track of files and folders on the disk.
The Attribute B-Tree is new in HFS+ (Mac OS Extended), and is not really used quite yet, except (I believe) in a very limited way by Tiger's Spotlight. The Attribute B-Tree is not used to store information about where the files are located on a disk. It is, in theory, used to store "metadata." In a future version of Mac OS, Apple has talked about allowing you to tag a file with any sort of descriptions, comments, or keywords that you want. For example, you could write a letter to your mother in Microsoft Word,and you could save it as "letter-to-mom.doc" with the tags "family," "mother," "personal letters," and "recipes for pie." You could then, for example, use Spotlight to say something like "Find a list of all files on my hard drive that are personal letters" or "Find a list of all files on my hard drive that have something to do with my family." Spotlight would search the attributes B-tree looking for those attributes, and find the files.
Right now, Spotlight can not do this. It can search for words inside a file, but if the letter you wrote to your mom does not contain the word "family," then Spotlight won't find it. With attributes, you can tag files with names or keywords or any other kind of association and Spotlight will find it. You could even, for example, make a Spotlight "smart folder" with the attribute "family," and whenever you open that folder, all your files that have something to do with your family would be inside it.
But that has not been implemented yet. The Attributes B-tree is not really used for anything of note yet. I don't know if Leopard will make use of file attributes or not.
