The important part to mention here, is that for Anycast to be of benefit, you would be doing it at geographically diverse locations. There wouldn't be a point of doing anycast at the same physical location (a load balancer or other methods would be prefereable). This allows you to bring your content closer to end users.
From a technical perspective, a provider "announces" the same IP space at different locations which they will assign to your VM's (each VM will have a standard public IP which routes directly to it, and the anycast IP which will be assigned to all of them).
This does introduce some extra nuances in your application that you will need architect around. If you're using it for simple static files (like a CDN) this isn't really an issue. If your application tracks user sessions, it can be possible that your end user may hit different physical servers in some situations. For example, if you have end users who are on a corporate network where their LAN admin does simple outgoing "load balancing" through different ISP's, the potential is there that each load balanced packet would end up on a different server. So setting up an internal network between your VM's and sharing some common aspects of the application is important in this case.
There are many benefits to anycast (especially if your content is latency & bandwidth dependent), but there is also much more to be aware of at the network level as well.