Intrinsic motivation refers to doing an activity for its inherent satisfaction rather than for some separable consequence. When you are intrinsically motivated, you engage in an activity because you find it interesting and enjoyable, not because of external pressures or rewards.

Let's evaluate each option to determine which one exemplifies intrinsic motivation:

1. Motivation driven by personal interest or enjoyment of the task: This option perfectly describes intrinsic motivation. When an individual engages in a task out of personal interest or enjoyment, it signifies that the motivation comes from within, matching the definition of intrinsic motivation.
2. Motivation driven by competition with others: This is an example of extrinsic motivation. The drive is influenced by external factors such as outperforming others, which is different from being motivated by internal satisfaction.
3. Motivation driven by gaining the appreciation of others: This reflects extrinsic motivation, where one's actions are influenced by the desire for external approval.
4. Motivation driven by external rewards: This is the essence of extrinsic motivation because it relies on external rewards rather than internal satisfaction.

Therefore, the correct answer is: Motivation driven by personal interest or enjoyment of the task.