When creating a database using an ERD, what do the entities and relationships become (in database terms)?
When implementing an ERD as physical database the following mappings apply:


An entity becomes a table (set of rows)
A relationship becomes a foreign key. 
Associative (many to many) relationships become a table with a foreign key to each associated table. 


Generally the ERD shoud be in at least third normal form.  

A few notes about relationships:


The (zero or) one side of the relationship is implemented as the  primary key of the table. 
The many side of the relationship is usually implemented with a foreign key index. 
If the site opposite the many side range is zero to one, the foreign keys column(s) are nullable. 
If the side opposite the many side range is one to one, the foreign key columns are not nullable.
If the side opposite the many side range is also zero or one to many, then a relationship table must be implemented.


Many ERD tools can be used to create the tables and indexes; or the DDL (Data Definition Language) to do so.  They may also be able to create an ERD from a database.  The best tools can update an existing database to match a modified ERD, or generate the DDL to modify the database.