Now let us talk about a windows based system where the OS contains a File allocation Table or FAT in short. This is a system that helps the computer to keep track of location of the files. This allocation system also makes it easier to find where you have kept your files and folders. While a folder system is for the user to manage his files, a directory system is used by the computer as a way of organizing all the information that you keep inside, in a manner similar to a telephone directory.
To give you an example, the hard drive of a computer is divided into sections called, C drive, D drive, E drive and so on. Taking C drive, we find that there are your downloads, program files, drivers, OS (whichever you use), temp, and so on.
When you right click on any folder and check its properties, the computer always shows its path as C/My Documents/Downloads and so on which gives you an idea of the directory system used by the computer. Users are also helped by this directory system as they can check different partitions of their hard drives to see where there folder is finally stored.
Apart from this simple explanation, there are many technical differences also between folder and directory.