Typically, computers and devices connected to the internet are uniquely assigned an IP address, this is called Unicast.
Anycast on the other hand, allows the same IP address to be assigned to multiple servers, not necessarily located together. When a request is sent to an IP it is routed to the closest server. If one of the servers is down the request is seamlessly routed to the next computer. This can have many advantages!
Anycast lends itself to services like CDNs and DDOS protection.