C++ FAQ Celebrating Twenty-One Years of the C++ FAQ!!!
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Section 7:
[7.1] What is a class?

The fundamental building block of OO software.

A class defines a data type, much like a struct would be in C. In a computer science sense, a type consists of both a set of states and a set of operations which transition between those states. Thus int is a type because it has both a set of states and it has operations like i + j or i++, etc. In exactly the same way, a class provides a set of (usually public) operations, and a set of (usually non-public) data bits representing the abstract values that instances of the type can have.

You can imagine that int is a class that has member functions called operator++, etc. (int isn't really a class, but the basic analogy is this: a class is a type, much like int is a type.)

Note: a C programmer can think of a class as a C struct whose members default to private. But if that's all you think of a class, then you probably need to experience a personal paradigm shift.