An object model is a structural representation of software 
objects (classes) that comprise the implementation of a 
system or application. An object model defines a set of 
classes and interfaces, together with their properties, 
methods and events, and their relationships. 

for more information go to the QTP Help.

By using QTP automation object model, we can automate QTP
operations.
By using object, methods and properties provided by QTP, we
can write programs that can configure QTP operations and
settings.
For example, you can create and run an automation program
from Microsoft Visual Basic that loads the required add-ins
for a test or component, starts QuickTest in visible mode,
opens the test, configures settings that correspond to those
in the Options, Test Settings, and Record and Run Settings
dialog boxes, runs the test, and saves the test. 

Test Object Model, is nothing but how QTP identifies the
objects in the application.
How to get the class of an object, what mandatory and
assistive properties are used during recording the
application, how it identifies the objects during run
session etc...