Azure Traffic Manager spreads the workload over multiple regions and data centers in the world. It will handle the load and locate the closest geographical region or most suitable region at the DNS level. The client makes a DNS request and, based on the location of the DNS, Azure Traffic Manager will locate the nearest region in Azure and sends that location back to the client via a DNS response. The client then calls the location directly, without any further interference of Azure Traffic Manager. Traffic Manager also monitors the endpoints, so in case of a failure inside one region, the Traffic Manager will send back the endpoint of a different healthy region.
This differs from the Azure Load Balancer, where the client calls the IP address of the Load Balancer and the Load Balancer distributes the traffic over multiple cloud services, such as VMs, containers...