What does a database expert mean when she says that a databse displays both entity and referential integrity?

Entity integrity, also known as a check constraint, is a database imposed restriction that the value of a field be limited. For instance, you could say that a number can only be in the range of 1 to 100, and the database would not allow you to insert or modify a row to have a value outside that range.

Referential integrity, also known as a foreign key constraint, is a database imposed restriction that the value of a field be contained in the primary key or a unique key associated with another table. For instance, you could say that a programmer's name be contained in a table of employees, and the database would not allow you to insert or modify a row to have a programmer that is not also an employee. In this example, to clarify, the employee table would contain people that are programmers, as well as analysts, managers, officers, etc.