1.1 - B-tree Basics
B-tree was invented back in 1971 by Bayer and McCreight (the B does not main anything know, speculations are that it comes either form the B of Bayer or from Boing they were working for back then). It was an extension to binary search tree, which was just able to store 2 elements per page.
A B-tree is a "tree data structure that keeps data sorted and allows searches, sequential access, insertions, and deletions in logarithmic time." (see Wikipedia)
The important point here is the last one : it guarantees O(logn) operations, compared to any other data structures (a hashed data structure offers O(n) average operations, but can degenerate to O(n2), and ordering is not kept. But there is more : by gathering N elements in a page, which leads to more comparisons than necessary, but still save a lot of disk accesses, as those comparison will be done in memory when a page is fully loaded. That's the reason for B-trees to have been invented.
B-trees are everywhere : databases, OS, etc. It's a critical data structure when you are to deal with a huge number of data.
1.1.1 - Inside a B-tree
A B-Tree contains Nodes and Leaves. A Node points to other Nodes or Leaves. Leaves contains Values. Both Nodes and Leaves have Keys that are associated with Values. Keys are not copied in many pages, they just appear once in the whole B-tree.
Pretty simple !
One last thing : Keys are ordered, and this is the condition for the easy and fast retrieval of Values.
A few more rules are enforced : A Node and a Leaf contains up to N values (N being generally a power of 2, so 2, 4, 8, 16...). You can't have less than N/2 Values or keys in a Leaf or a Node, except for the root Node.
1.1.2 - Concurrent access
The real problem with B-trees is that we need to use some locks to allow concurrent access to the data, especially when some updates occur. The rational is that when browsing a B-tree, changing it will just break the browse operation. There are some technics to avoid having such an issue, up to a point no read locks are needed, assuming some extra information is added to the pages : a pointer to the next page at the same level. Sadly, it comes with drawbacks, like it's difficult to remove empty pages from the B-tree.