I have gone through the Wikipedia definition several times:
A database engine (or "storage engine") is the underlying software component that a database management system (DBMS) uses to create, read, update and delete (CRUD) data from a database.
What I don't understand is what is left to do, isn't CRUD all that the databases do?
If the database engine performs these functions, what does the rest of the database do?
CRUD is meant to define the characteristics necessary for a database as it relates to persistent storage. It is not meant to describe everything that could be done by a database engine.
To make a comparison, fundamentally a vehicle is a device used for transport. While true, this definition certainly doesn't include all the detail entailed in a modern automobile.
A database engine might handle multiple users, transactions, MVCC (Multiversion Concurrency Control), buffers and caches, ACID (atomicity, consistency, isolation, durability), as well as different isolation levels. A read may pull data from memory, remote databases, and multiple tables on disk processing it using SQL through multiple explicit and/or implicit code paths in order to present it to the requesting application. A create may allocate storage, provision structures, assign values, and do it's own processing before storing data. Etc.
Some databases can run many engines, depending on the best fit for the job. For example, many of my applications use InnoDB for most data (key constraints and row level locking), MyISAM for session data (fast, less processing) and ArchiveDB for audit trail (compressed and insert/select only, no update/delete).
The "rest" of the database software provides a common interface for use through APIs or terminals, allows complex actions (like joins, subqueries, etc.) and manages the health/status and configuration of the included engines. There is a lot to the feeding and care of an engine, and the database software hides all of that complexity.
