The System Integration Testing(SIT), also known as
integration testing, is the phase of software testing in
which individual software modules are combined and tested as
a group. It follows unit testing and precedes system
testing. Integration testing takes as its input modules that
have been checked out by unit testing, groups them in larger
aggregates, applies tests defined in an Integration test
plan to those aggregates, and delivers as its output the
integrated system ready for system testing. The purpose of
Integration testing is to verify functional, performance and
reliability requirements placed on major design items.

System Integration Testing (SIT) is the testing of the sub-
systems, as a whole, to ensure that they work as a system. 
It is accomplished whenever multiple systems cross 
functionality & external interface level testing is 
required. Also, verifies that the system is integrated to 
any external or third party systems defined in the system 
requirements.

When it comes:

Unit testing-> Integration testing -> System testing -> 
System integration testing.

Example:
I would like to explain about this SIT by taking a banking 
application:

consider ICICI online banking application(these assumption 
may not be true in real applicationi of ICICI):

Hope the reader know about the Loans: let's us consider 
that a person came to take a personal loan from the bank

How the bank gives the loan it will consider certain 
criterias like his previous bank statements his balances, 
his properties, credit card bill payments etc etc..

1) unit testing: the developer will test the application( 
front end) after he is done with the code.

2) Integration testing: considering this as a client server 
application. Testing whether the front end information 
(like values, addresses etc) are reflecting in the back end 
bye checking at the back end and vise versa by checking at 
the front end.

3)System testing: testing this application (system) as a 
whole and based on the functionality. checking whether the 
info giving at the front end is reflecting again at the 
front end where ever necessary.

4)System integration testing: suppose in this appication to 
generate the instrest information , payment information , 
etc if we are using some other application which is not 
related to this application but integrated to this to 
fulfill some task so testing this all functionally as a 
whole.

still if you need any further info plz post again,

thanks.