On some CMS systems, you can track customer's behaviour (pages accessed, search queries performed, etc). Does SharePoint 2013 have similar?
An example is to review the 10 most reviewed webpage in January, etc.
You're thinking the SharePoint Usage and Health Service Application which gathers up much of this data and gives a few basic reports and can be customized via SSRS for more. So likely yes it can do what you say.
You can control access to this via standard SharePoint permissions.