What does 'right heart' failure mean?

Right heart. In right heart failure the right side of the heart (aka right ventricle) is affected and weakened. It can occur as consequence of pulmonary hypertension, or severe lung disease (cor pulmonalae) or end stage left sided failure.
Right Heart Failure. Essentially the right ventricle is weak and pressure within the veins builds up causing fluid to collect in the legs and abdomen. This is a very simplified answer to a much more complex process.