The terms "intrinsic" and "extrinsic" involve pretty typical scientific/medical root word language that appears in many other places, some of which are probably familiar to the average person. Specifically, the "in" in "intrinsic" basically means exactly what it sounds like: "inside." "Ex", just like "exit", means "outside". Intrinsic and extrinsic factors are, respectively, things that are inside or outside the system being discussed.
Intrinsic control of the heartbeat would refer to any type of control that arises from structures or properties of the heart itself. Extrinsic control arises from structures outside the heart.
To understand both control systems, it's necessary to understand how the heartbeat operates. Throughout the body, muscles generally respond to changes in electrical signals; most people are familiar with this through the common depiction of a person shaking due to electrical shock. In order for the heart to beat normally, a series of highly regulated electrical signals need to reach specific parts of the heart at specific times. There are aspects of this that are more flexible than others; for example, the entire sequence can be sped up, but it needs to maintain the same order of events, otherwise blood would flow in the wrong direction or not at all.
The sinoatrial ("SA") node is commonly pointed to as the source of the heart's intrinsic control. This is a bundle of cells that are capable of generating an electrical charge (an "action potential") by changing the amount of ion solutes present in the immediate area. These changes proliferate throughout the heart, triggering contractions. Other parts of the heart, such as the AV node, help this process to occur in a more controlled manner.
Extrinsic controls are more varied, but effectively, they could be seen as anything that exerts some kind of influence on the SA node. This could include factors from the endocrine system, signals from the nervous system, or drugs. The most direct way of extrinsically controlling the heart would be any means of modifying the concentration of calcium ions that the SA node is generating at a given time.