There may be an obstruction in the toilet that is causing it to half flush. A toothbrush comes to mind, where you would still get a flush but not a very good one.
Is this a new problem, has it flushed better in the past?
The water level in the tank may be low or the flapper in the tank could be closing prematurely.
It either needs an auger to clear, or a new flapper.
The Local Plumber
Tustin, California http://www.TheLocalPlumber.com