Anycast is a networking technique where the same IP prefix is advertised from multiple locations. The network then decides where to route a user request, based on routing protocol expenses and possibly the ‘health’ of the advertising servers. There are several benefits of anycast.
In steady-state, users of an anycast service (DNS is an excellent example) will always connect to the ‘closest’ (from a routing protocol perspective) DNS server. This reduces latency, as well as providing a level of load-balancing (assuming that your consumers are evenly distributed around your network).
Another advantage is the ease of configuration management. Rather than having to configure different DNS servers depending on where a server/workstation is deployed (Asia, America, Europe), you have only one IP address that is configured in every location.
Packet latency is largely a function of geographic distance (It has other impacting factors too). With Anycast, we tell routers the same server is located at a bunch of different spots around the internet. Because internet routers are always optimizing routes they pick the one closest to the requester. Moving DNS servers closer, mitigates this geographic latency component. While lower latency is one of the most important benefits of Anycast DNS, we will also gain resilience at the same time.