The /usr directory is the main application storage directory. All binary files in this directory must not be required for the system startup or maintenance, since the /usr hierarchy is very often located on a separate file system. Given its often large size, /usr has its own hierarchy of subdirectories. We will mention just a few:
/usr/X11R6: the whole X window system hierarchy. All binaries required for the operation of X (including the X servers) and all necessary libraries must be located here. The /usr/X11R6/lib/X11 directory contains all aspects of X's configuration which do not vary from one computer to another. Specific configuration for each computer should go in /etc/X11.
/usr/bin: this one holds the large majority of the system's binaries. Any binary program which is not necessary to the maintenance of the system and is not a system administration program must be located in this directory, apart from programs you install yourself, which must be located in /usr/local.
/usr/lib: it contains all the necessary libraries to run programs located in /usr/bin and /usr/sbin. There is also a /usr/lib/X11 symbolic link pointing to the directory which holds the X window system libraries, /usr/X11R6/lib (if X is installed, of course).
/usr/local: this is where you should install your personal applications. The installation program will created the necessary hierarchy: lib/, man/, etc.
/usr/share: this directory contains all architecture-independent data required by applications in /usr. Among other things, you will find zone and location information (zoneinfo and locale).
There are also /usr/share/doc and /usr/share/man directories, which respectively contain application documentation and the system's manual pages.