You will find in this directory, a log file for each Shinken daemon :
and an other more global :
Note : there is a daily rotation of log files (for X days by default but you can edit this in configuration ?).
Those files are also in this directory and they are suffixed with a date like this : arbiterd.log.2015-09-02
To launch Shinken in debug mode :
service shinken -d [debug level] restart
or (only one)
service shinken-[daemon name] -d [debug level] restart
In this one, you will find all events about your Shinken Architecture, because the arbiter daemon is used to check and dispatch configuration to the others daemons ( but not the Synchronizer ).

In error case :

Very useful in complex architecture with spare daemons where you will see here rocker events.
In this one, you will find all events about data management, because the broker daemon is used to export and manage data ( from schedulers ), for example, making those logs files ( and rotation ).
In this one, you will find all events about checks plugins, because the poller daemon is used to launch checks and return results to the schedulers.