What does Yoga have to do with willpower and discipline and how is it related to our daily lives?

In Yoga in this context we talk about Tapas. Word tapa is literally translated from Sanskrit as „to burn”.
Tapas has the sense of „cooking” ourselves in the fire of discipline to transform ourselves. It can be compared to a process of cooking an egg.
Tapas is our determined effort to become someone of character and strength. It’s a discipline to achieve something.

By using Tapas we train our willpower. Willpower is like a muscle - the more you train it - the stronger and resilient it becomes. With each successful goal you manage to achieve your willpower becomes stronger.

Ideally we all should practice Tapas regularly.
Start with something achievable. Slowly increase the difficulty and find your edge - you can stop eating sugar, quit smoking for at least 5 days, or start practicing yoga once per week.