When reading through the Hibernate documentation I keep seeing references to the concept of a "natural identifier". Does this just mean the id an entity has due to the nature of the data it holds? IE: A user's name+password+age+something are its identity?
What naturally identifies an entity. For example, my email address.
However, a long variable length string is not an ideal key, so you may want to define a surrogate id
AKA Natural key in relational design
A social security number might be a natural identity, or as you've said a hash of the User's information. The alternative is a surrogate key, for example a Guid/UID.
A natural identifier is something that is used in the real world as an identifier. An example is a social security number, or a passport number.
It is usually a bad idea to use natural identifiers as keys in a persistence layer because a) they can be changed outside of your control, and b) they can end up not being unique due to a mistake elsewhere, and then your data model can't handle it so your application blows up.