Route 53 is a DNS service provided by AWS. DNS is the abbreviation for Domain Name Server.
To understand Route 53, you will first have to know what is DNS.
I will give a simple example. So, every server has an IP address. To go to the google website, you just type in google.com and it takes you there. So, here google.com is the domain name.
Let's assume there is no DNS server, then you will have to remember the IP address of google and then enter to go to their website. But we use a lot of websites and we cannot remember all the IP addresses. That's where a DNS server helps. A DNS server stores all the IP address and has the corresponding domain names. Now, if you enter google.com, this request is sent to the DNS server which will check the corresponding IP address and take you to the website.
That is what Route 53 does. You can create a Hosted Zone which is basically redirecting traffic to the respective IP addresses when the domain name you have is typed in the browser.
For more information, check out this informative AWS Route 53 blog.