A SharedLibrary contain subroutines that can be linked to a BinaryExecutable at RunTime. This allows for sharing code between applications, which has a number of advantages:
$ ldd /sbin/mke2fs
libext2fs.so.2 => /lib/libext2fs.so.2 (0x40023000) libcom_err.so.2 => /lib/libcom_err.so.2 (0x40037000) libe2p.so.2 => /lib/libe2p.so.2 (0x40039000) libuuid.so.1 => /lib/libuuid.so.1 (0x4003e000) libc.so.6 => /lib/libc.so.6 (0x40041000) /lib/ld-linux.so.2 => /lib/ld-linux.so.2 (0x40000000)
$ ldd /sbin/init
not a dynamic executable
$ otool -L /bin/zsh
/usr/lib/libncurses.5.dylib (compatibility version 5.0.0, current version 5.0.0) /usr/lib/libSystem.B.dylib (compatibility version 1.0.0, current version 60.0.0)
This creates a SharedLibrary file libfoo.so.1.0.1, with shared object name ("soname") libfoo.so, dependent on libquux. To make libfoo usable, you need to put it someplace ldconfig(8) will find it, and SymLink it to libfoo.so.1 and libfoo.so.
So long as you don't change the call signature of one of the functions (or what they do, in a way that would break programs), you can just bump the minor version of the library and programs using the SharedLibrary will just work. If you do change call signatures on existing functions or change their semantics, bump the version, try to recompile the programs, and check that they work correctly once they pass.
For more information, see Ulrich Drepper's How to write shared libraries.