Do you mean the Integer class, or do you mean a file called "int.class" that you have on your harddisk?
Im assuming you mean a file int.class in the following:
When you wan't to make a program/application in Java, you start with a Java file, e.g. Int.java. In this file you write Java code. When you have written enough code, you have to "compile" the java file, which you do by the following command: >javac Int.java
That will create the file "int.class", assuming there arn't any errors in the code of Int.java.
Back to your question: a .class file is bytecode, and contains everything the Java Virtuel Machine (JVM) needs to know about your java class.
For more information about the organization of the .class files I'd recommend you to goto Javaworld and search for "class file".
How do you use it? Assuming the java class has the "static void main(String args)" method you can execute with the following command: >java int
If the java class is more of a "helper" class, you can use the class in your programs. Just as you use the normal Java classes like Vector, Math and so on.