What is the difference between /opt and /usr/local directories?

/opt is for third-party applications that don't rely on any dependencies outside the scope of said package. /usr/local is for packages installed on this machine outside the scope of the distribution package manager.

An example:

An open source sip-client supplied as a .deb would install into /usr. If it was built with the Qt framework, apt would pull it in as a dependency.

The same open source sip-client built from source would reside in /usr/local. So it would not be messed up by apt if you later installed a .deb package for the same application. You could either build its dependencies from source, or get them from the package manager.

A third-party application in /opt is supposed to be self-contained. For instance, a proprietary sip-client using Qt would not rely on the version from apt, but would have it bundled or statically linked in.