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.
In Microsoft products and technologies, multi-tenancy of services creates a hosting environment wherein server farm resources are maximized. Before learning about hosting environments, it is important to understand the services architecture.
General guidance for hosters in SharePoint Server 2013: https://technet.microsoft.com/en-us/library/dn659287.aspx
If anybody is looking for documentation or the complete process of setting up a SharePoint 2013 Enterprise server for Multi Tenancy then I would suggest looking at the following set of articles by Spence Harbar.
The first is his walk through for how to build a multi-tenancy environment in 2010. The second is a newer blog post on what changed in 2013. I don't think I've seen anyone do a full walk through specifically for 2013.