Database storage engine is the component that determines how data is going to be stored on the disk and knows how to retrieve information from the DB. Databases usually come with one or more storage engines and let you switch between them depending on your requirements.
Storage Engines generally handle the following :
and more..
On a side note you should choose a storage engine based on your needs i.e. there is no best storage engine. For example, at Hashnode we are using WiredTiger storage engine (MongoDB) as we want document level locking. Many other companies will probably be fine with MMAPv1.