They are constant values, once they are created they cannot be changed
From
Java Tutorials — Enum Types:
An enum type is a special data type that enables for a variable to be a set of predefined constants. The variable must be equal to one of the values that have been predefined for it. Common examples include compass directions (values of NORTH, SOUTH, EAST, and WEST) and the days of the week.
Because they are constants, the names of an enum type's fields are in uppercase letters.
Later on:
Each enum constant is declared with values for the mass and radius parameters. These values are passed to the constructor when the constant is created. Java requires that the constants be defined first, prior to any fields or methods. Also, when there are fields and methods, the list of enum constants must end with a semicolon.
Your teacher is correct, they are referred to as enum constants. It does make sense, because enums are the datatype made to represent a fixed set of constants.
I hope that helps
Edit: note that your example of an enum is an example on the page I linked to; I think it probably comes from there.