What is Amazon Route 53 and how does it work in AWS?

I'm learning AWS and cloud networking, and I often hear about Amazon Route 53 for managing domains and directing internet traffic. I understand it's a DNS service, but I'm not sure how it works or why developers use it instead of traditional DNS providers.

Can someone explain what Amazon Route 53 is, how it works, and its key features, such as domain registration, DNS routing, health checks, and traffic routing policies? I'd also appreciate a simple real-world example showing how Route 53 routes users to web applications hosted on AWS.