What is Azure private peering?

Azure compute services, namely virtual machines (IaaS) and cloud services (PaaS), that are deployed within a virtual network can be connected through the private peering domain. The private peering domain is considered to be a trusted extension of your core network into Microsoft Azure. You can set up bi-directional connectivity between your core network and Azure virtual networks (VNets). This peering lets you connect to virtual machines and cloud services directly on their private IP addresses.