To answer this question, you might firstly want to explain what lifespan development is, as this is obviously crucial to explain your interest in this matter. Lifespan development is part of developmental psychology. It looks at how people grow and change throughout their lives, starting right at the start at conception and leading up right to death.
One of the reasons why many people find lifespan development important is because it looks at several issues that impact on a person's development rather than individual issues in isolation. Lifespan development includes cognitive, physiological, emotional, and social development. All of these are important factors in a person's life and play a huge part in determining a person's actions, thoughts, and feelings.
In terms of what you might hope to learn about, you might want to mention that you might be interested in finding out more about yourself. Learning about lifespan development will enable you to look at life in a slightly different light, which may well mean that you will also discover a lot about yourself. For example, you might understand as a result of your studies why certain events in your life have happened, or why they happened the way they did.