Auth.log in Debian Systems
Your auth.log file is the first step in determining of an intrusion is being attempted, or has occured. It logs all ssh connection attempts, cron jobs, and su calls. If an ssh brute force attach is occurring you will see countless failed ssh login attempts. Most likely various usernames will be attempted. You should immediately stop the ssh server and implement some security countermeasures. Implement various rules in your hosts.allow and hosts.deny files any if you want implement some iptables rules. Host.allow and deny should be enough; the files control tcp connections to your running system daemons. Iptables will block ip numbers just at the connection attempt is made to the computer so for ultimate security implemente iptables and various host rules.
After locking down your servers you will see brute force attacks stop, and your auth.log file will be mainly filled with cron jobs and su commands by users and daemons. The cron jobs are automated process run by various applications, and are mostly run as root. Mail servers, and other tasks are typically managed by cron jobs. You can check user specific cron jobs using the crontab command. Use option -e to edit a users jobs.