Quadrable is an authenticated multi-version database. It is implemented as a sparse binary merkle tree with compact partial-tree proofs. There are C++ and Solidity libraries, as well as a git-like command-line tool.
The reason we use trees is because of the exponential growth in the number of nodes as the number of levels is increased. In other words, the number of intermediate nodes that must be traversed to get to a leaf grows much slower than the total number of nodes.
For some reason, computer science trees are usually drawn as growing in the downwards direction. Because of this, we use the term "depth" to refer to how many levels down you are from the top node (the "root").
In a merkle tree, each node has a "nodeHash" which is formed by hashing the concatenation of its children nodeHashes. In Quadrable the tree is binary, so there are always exactly two children (except for leaf nodes, which have none). The order of the concatenation is important: The left child's nodeHash comes first, followed by the right child's:
The advantage of a merkle tree is that the nodeHash of the node at depth 0 (the top level) is a digest of all the other nodes and leaves. This top-level nodeHash is often just called the "root". As long as the tree structure is carefully designed, and the hash function is secure, any changes to the tree or its contents will result in a new, distinct root.