BIN.h implements a logarithmic bin layout to pack your binary tree into a flat buffer. The layout looks like this:
---- 7----
/ \
/ \
3 11
/ \ / \
1 5 9 13
/ \ / \ / \ / \
0 2 4 6 8 10 12 14
Cell index calculations are cheap, typically some arithmetics and bitwise ops. Performance-wise, one can see such a tree as a random access array.
Overall, ABC C advocates the use of buffer-based data structures to improve code composability. For example, one can mmap a BIN based tree from a file, checksum it and send it over the network, all using generic routines. No OOP, no interfaces, just buffers and library procedures. Other examples of the approach are binary HEAP, LSM iterator heap and HASH set.
Originally, the layout was devised in Nov 2008 to host binary Merkle trees for multimedia streams.
BIN.h dates back to those times, save for minor convention tweaks.
Later, the layout made its way into some internet drafts and RFC 7574.
Recently, Russ Cox made a good writeup discussing all ways of packing a tree into a buffer.
BIN specifically implements in-order traversal of binary trees (there are many other options).
There is a bunch of implementations of the same scheme by M.Buus and friends.