What are patron-client systems?

I assume that you are asking about the social/political
system known as the patron-client system.  In such a system, social and political
systems are bound together by very personal ties between clients and their patrons.  The
patrons ae supposed to act almost like parents to their clients.  In return for the
clients' loyalty and political/social support, the patrons are supposed to provide for
the material needs of the clients.

This sort of system can,
for example, be seen in places like Mexico.  In Mexico, there have historically been
elites in each area who dominate the politics and society of their regions.  These
people rely on their clients for political support, for labor, and at times for military
support to keep them in power.  In return, they are supposed to help their clients get
jobs, education for their children, and other such
benefits.

In other words, a patron-client system is one in
which the leaders and the followers have a personal connection rather than a more
legalistic, impersonal connection as is typical in places like the
US.