I believe the phrase is quite self-explanatory. Here's a breakdown:

Entity: Represents a table in a database > Attributes: Represent the columns of the table > Record: Represents the data stored in a row of the table.

In this context, the "record of an attribute" refers to the data stored in a specific column for a particular row. An entity can be seen as the overarching boss,  while attributes and records are its components.

Agree it should be record of an entity.  Record refers to a set of attributes, not a single attribute.