An anatomical lever system is using the body to increase intensity. For example, lifting a weight with the arm straight vs. the arm bent, increases the intensity. The lever being the arm. The further away from the body the load, the weight, is, the more intense, difficult, the exercise becomes. Any body part can be a lever, as long as it moves around a joint. The further from the joint the part is being lifted, the more difficult the exercise.
A mechanical lever system in exercise usually refers to using a piece of equipment to act as the lever. Think of leg extension machines at the gym. The laws of the lever system are still the same in both.
Here’s a great explaination of how the lever system applies to exercise: