Add-ons can then log activity and errors there for the administrators to monitor.
Add-ons can choose which log level to send - for example informational updates (eg "X number of emails sent by this cron entry") or debugging ("output from this SOAP call").
The logging facility would implement the standard PSR-3 log levels (emergency, alert, critical, error, warning, notice, info, debug) and the UI would allow filtering log messages by date, PSR-3 log level and/or add-on id.
Also, the administrator would be able to set a minimum log level to actually get stored (eg only warning and above), so that spurious debug and info logs don't fill up the database on production servers.
Add-on developers could also potentially extend the capabilities of this core logging facility to send log information to external application monitoring systems (eg New Relic) or even just to notification systems (HipChat, Slack, etc).
Implementing a PSR-3 interface would also allow us to wire external packages (eg payment gateways, integration libraries, etc) to the logging system such that any log messages they send will automatically end up in the XenForo log - even if those packages were not built with XenForo in mind.