However, I got curious to what each class contained and when I try to open one of the classes in the jar file, it tells me that I need a source file.
A jar file is basically a zip file containing .class files and potentially other resources (and metadata about the jar itself). It's hard to compare C to Java really, as Java byte code maintains a lot more metadata than most binary formats - but the class file is compiled code instead of source code.
If you either open the jar file with a zip utility or run jar xf foo.jar
you can extract the files from it, and have a look at them. Note that you don't need a jar file to run Java code - classloaders can load class data directly from the file system, or from URLs, as well as from jar files.