It was announced by Miguel de Icaza, the project lead for Mono (the open-source implementation of the .NET Framework) that the MonoDroid beta is now open for public access. MonoDroid is an abstraction layer on top of the Android SDK that allows .NET developers (mainly those who program in C#) to create Android applications without directly touching Java code but rather work directly with C# and .NET-compatible types and structures.
Some features are currently missing from the library set (as per Miguel):
We use a library profile that is better suited for mobile devices, so we removed features that are not necessary (like the entire System.Configuration stack, just like Silverlight does).
However, you are still able to use some of the most widely accepted .NET features, like LINQ. OpenGL is supported in the context of the OpenTK library.
Currently, you can only use MonoDroid on Windows coupled with a Visual Studio development environment. You will still need the Android SDK installed, so don't expect MonoDroid to be a complete replacement for the tools distributed by Google.
If you are new to MonoDroid, you should definitely check out the mailing list. I've been a member of it since private beta and I must say that a lot of the discussions regarding bugs, workarounds and additions are going over there first, so it should be the primary informational tool on the new platform for you as a developer.
Also, you can check out the MonoDroid docs (some sort of MSDN Library) here.
You can find the original article by Miguel de Icaza here.