/ - Root: All files are under this.
/bin - Binaries: Contains the executable files of many basic shell commands.
/dev - Device: Contains special files.
/etc - Etcetera: Historic name. These days contains configuration files.
/usr - User Binaries: All the executable files, libraries, source of most pgs.
/home - Home: User personal space. 
/lib - (Shared) Libraries: Codes that can be used by the executable binaries.
/sbin - Sudo Binaries: Same as /bin but for root level binaries only.
/tmp - Temporary: Applications use this directory to store temporary files
/var - Variable: Programs store runtime information like system logging...
/boot - Boot: Contains files of the kernel and boot image.
/proc - Proccess: Information about currently running processes and kernel.
/opt - Optional: Installing/storing the files of third-party application.
/root - Root: Root user's personal space.
/media - Media: Mount point for USBs etc..
/mnt - (Manual) Media: For manual mounting.
/srv - Contains data for services provided by the system. (i.e. HTTP Server)