You have 3 types
1) the Audit Trail – Some orgs use this for tracking who runs which runbooks and when. This is enabled from the command line on the management server.
2) Activity Level Logging (which is what I use most often), which shows you where runbooks fail and some details of output. This is enabled in the properties of the runbook in the Runbook Designer interface
3) Debug logging, which is enabled in the registry. This provides verbose output of runbook activity at an activity level, if you set the verbosity high enough (1 default, 7 max).