I often read about Nginx and Mongrel being used together. Can someone explain to me how they are different? Why is Mongrel needed? Why is it not advisable to have Nginx directly communicate to the many Rails servers?
Both are web servers, but they do not share the same focus :
To be clear, your rails app by itself isn't directly usable, it needs what you can call a container (I suggest you read some about http://rack.github.com/), in this case Mongrel. When you run rails console, it's usually webrick, the most basic web "app" server we have in Ruby (it's part of the standard library).
Then why do we use Nginx in front ? Let's consider we use only Mongrel : we fire a mongrel instance, listening on the port 80. If your requests takes for example 500 ms to complete, you can handle 2 clients per second any nothing more. But wait that's clearly not enough. Let's fire another mongrel instance. But we can't have it listen on the port 80 since it's already used by the first instance and there's nothing we can do about it.
So we need something in front that can handle multiple Mongrel instances, by still listening the port 80. You throw in a Nginx server, that will (proxy) dispatch the requests to your many mongrel instances and you can now add more instances to serve more clients simultaneously.
Back to answering your question, having NGinx communicating to a rails server, means firing one or many Mongrel (or Thin / Unicorn, whatever server is available) and informing NGinx it has to pass the requests to them. It's a popular pattern to host rails services next to using Passenger, which basically provides a way for Apache workers to handle ruby code.