The classes, here, are study units. A class in English, one in History, that would be two classes.
Community Colleges are generally smaller places of education, post secondary (after high school) attended by those who prefer to learn a trade, often, rather than, say, a PhD (a doctorate degree). Many students at community colleges will be adults taking just one course (class) at a time, say, in Japanese. They don't expect a degree or a diploma, they simply want to learn that particular subject.
It is generally easier to gain admission to a Community College; they have lower minimum standards of admission because they are dedicated to serving the immediate community. One would not often go far to attend a Community College.
In Canada, colleges (community and otherwise) grant "diplomas" and universities grant "degrees" at the end of a structured program.