The Managed Metadata service in SharePoint Server 2013 provides central term storage and management. The Term Store is what allows you to have common sets of terms that can be shared across all sites and site collections within a farm. The Managed Metadata service only comes with the pay versions of SharePoint Server; it is not available with SharePoint Foundation 2013.
Term Store terms are organized within a Term Set, which is created within a Term Group forming a hierarchy nested within the Managed Metadata Service. The parent service defines Term Store Administrators that are responsible for creating the Term Groups. The Term Groups define the Group Managers and Contributors.
Once Term Sets have been defined within the Managed Metadata Service, they can be linked to lists and libraries through a Managed Metadata column type. Managed Metadata columns create fields on the SharePoint forms that are linked to the Term Sets and provide IntelliSense that provide users with choices of terms based on what they type.