As per my definition LOG LEVEL means a way to differentiate the importance of logs in our application. We can divide the logs into categories based on their importance and effect for e.g. ERROR logs are more important than DEBUG logs.
Why do we need to print logs based on LOG LEVEL ??
It is really helpful in projects with millions of lines of source code where the user can't use #defines or #ifdef's in order to maintain DEBUG prints. It is really tiresome to maintain #defines and #ifdef atleast for printing logs.
printk which is a part of LINUX KERNEL supports printing logs based on LOG LEVEL and it is really helpful in debugging kernel.
printf or any of its brothers & sisters don't support the option to print logs depending upon the log levels.