For what purpose do we use Debug Logs in Salesforce?

In order to debug and understand the flow of automated processes in user perspective with system context.

You can debug Apex classes, Apex triggers, workflows, approval process and also define configure trace flags and debug levels.

Please check: https://help.salesforce.com/articleView?id=code_add_users_debug_log.htm&r=https%3A%2F%2Fwww.google.com%2F&type=5