A directory within a filesystem which appears within another directory. Obviously, every directory except the root directory is a subdirectory of some other directory, which is usually referred to as its "parent directory".

A pictorial example to explain these concepts:

        _ / _
       /     \
     home     usr
     /  \      \
    mel jason  bin
         /  \
        bin porn

Here, home and usr are subdirectories of /, and also pictured are two subdirectories of home and one subdirectory of usr. Unlike the author's actual computer, the directory /home/jason is the parent directory of porn (in reality, it's hidden way further down in the directory tree than that).