The Mono Project is an open source project to build C# and .NET desktop and ASP.NET applications for Linux and Mac OSX.
MonoDevelop is an IDE primarily designed for C# and other .NET languages. MonoDevelop enables developers to quickly write desktop and ASP.NET Web applications on Linux, Windows and Mac OSX. MonoDevelop makes it easy for developers to port .NET applications created with Visual Studio to Linux and to maintain a single code base for all platforms.
You can learn more about MonoDevelop here:
http://monodevelop.com/
You can compare MonoDevelop as Visual Studio IDE for Linux and Mac.
The Mono project, MonoDevelop, MonoTouch, and MonoDroid products are developed by Novell.
MonoDevelop 2.4 was released recently. Read here what is new in MonoDevelop 2.4
http://monodevelop.com/Download/What's_new_in_MonoDevelop_2.4
Here are some more readings on related topics:
What is MonoTouch by Mahesh Chand On Feb 10, 2010
MonoDroid - Develop Droid Applications using C# by Mahesh Chand On Nov 07, 2010
Here are some MonoDevelop related FAQ
Q: What is difference between Visual Studio 2010 and MonoDevelop?
A: MonoDevelop is an IDE developed by Novell. Visual Studio 2010 is an IDE developed by Microsoft. Visual Studio 2010 is still the best IDE out there but it cost you a lot. Also, Visual Studio does not support Mac and Linux. MonoDevelop works on Mac.
Q: Is MonoDevelop Free?
A: YES.
Q: I already have Visual Studio 2010. Do I still need MonoDevelop?
A: NO. Unless you are building iPhone or iPad applications using MonoTouch.