To perform network analysis, ArcGIS Pro requires a network data source. The network data source can be a network dataset in a geodatabase that is stored locally on disk or in a shared network location or it can be the URL to a portal, either ArcGIS Online or your own enterprise portal configured with routing services.
Routing services allow you to solve the same types of problems the ArcGIS Network Analyst extension allows you to solve: route, closest facility, service area, location-allocation, origin-destination cost matrix, and the vehicle routing problem. They allow you to share network analysis functionality across an organization without requiring each user to have an ArcGIS Network Analyst extension license for ArcGIS Pro. They also eliminate the need to manage multiple copies of the network dataset. Everyone in your organization uses a single authoritative source for all your network analysis.
When using routing services, there are two sources from which to choose: routing services available with ArcGIS Online or running these services on-premises using ArcGIS Enterprise.