Intrinsic rhythm is the rate at which the heart beats with no interference from the Central Nervous System. Cells of cardiac muscle, when left to themselves, will beat at variable rates. The heart has two structures, the Sinus node and the Atrial ventricular node that even out the rate of all the cardiac tissue. The rate provided by these two structures is around 100 bpm.
The fact that our hearts usually beat at around 60-80 bpm is due to the influence of the parasympathetic nervous system, specifically the Vagus Nerve, which innervated the heart and constantly sends messages to slow down the rythm. The sympathetic, or adrenergic nervous system, also innervated the heart and can push the rate up way past the normal rate of 100 bpm.