What is multi tenancy in share point 2013 and its architecture and multi-tenant site collections.
what are the main differences between share point normal publishing web application for public users who will access it by anonymous authentication?
You don't need to worry about multi-tenancy unless you are a cloud provider and you want to set up fewer servers. Another way to say it, if you have 100 SharePoint servers, then this feature would provide economies of scale. See below for the official Microsoft definition and supporting links.
From Microsoft Multi-tenancy refers to the ability to manage and partition data of sites and otherwise shared services or software in order to accommodate multiple tenants. This is in contrast to running multiple instances of a service, or setting up separate hardware. site: https://technet.microsoft.com/en-us/library/dn659286.aspx?f=255&MSPPError=-2147217396
Multi-tenancy is a Cloud Concept mostly holds by Hosting providers such as Microsoft (SharePoint Online) ,FPWEB, Rackspace etc.… site: https://manojviduranga.wordpress.com/2014/08/01/step-by-step-article-series-for-creating-sharepoint-2013-based-multi-tenant-private-cloud-infrastructure/