A Register is a dataset for a single kind of thing. It has the ability to provide previous versions for the data held in it.
Each entry defines a change for an element in the dataset by recording the time the change was appended to the log, the numerical order in the log, the key to identify the element the change is for and the reference to the data for that element.
A Register uses a sidecar data structure derived from the log that allows anyone to efficiently audit the integrity of the data held in it. This data structure is a Merkle tree as described by the Certificate Transparency RFC6962. Check the Audit section for details.
In summary, the log and all its parts form an immutable data structure that allow expressing a sequence of changes on the dataset of elements, the Register.