One IP address, hundreds of servers
Normally, one IP address maps to one physical server. If that server is in New York, a user in Tokyo experiences high latency on every DNS query. Anycast solves this at the network routing layer.
With Anycast, the exact same IP address is simultaneously announced by servers in dozens or hundreds of locations worldwide. The internet's routing protocol (BGP) automatically directs each query to the topologically nearest server announcing that IP. The client has no idea this is happening — it just gets a fast response.
Cloudflare's 1.1.1.1 and Google's 8.8.8.8 are both Anycast addresses. When you query 1.1.1.1 from Tokyo, you reach a Cloudflare data center in Tokyo or Singapore. When someone in London queries the same 1.1.1.1, they reach a data center in London or Amsterdam.
Why this matters for reliability: If one Anycast location goes offline or is overwhelmed by a DDoS attack, BGP routing automatically shifts traffic to the next nearest location. The IP address never changes, so clients don't need to be reconfigured. This is why major DNS providers can absorb massive DDoS attacks that would take down a single-server deployment — the attack traffic is distributed across hundreds of locations, each absorbing only a fraction of the load.