This is can be a rather complex question but, I'll try to explain it as simply as I can below.
To understand the history of the life here is to better understand the world we live in. Let me break it down.
Lets look at the bacterial level. When scientists and researchers study bacteria to create medicines to help prevent disease and sickness, they have to look at the history of the life of the bacteria to see how long it takes to adapt to this or that. When they do this it helps them to better understand how the bacteria works and how to formulate a cure for it or a preventive measure.
Understanding the history of most other living things on Earth can help us to better prevent further extinction of species and, for some that are on the verge of it, to help them rebound.
As for humanity, a lot of it is to better understand our ancestors, to understand how we became who we are today. Sometimes it's an extremely educational and fascinating trip through the history of life on this planet. How did it survive through the harshest of environments. How did this species survive when all these perished. How did this species thrive in this environment when nothing else can even survive there.
There are more reasons but this should give you a general idea of it.