Ok, what is Mono? Mono is an open development initiative that is attempting to develop an open source version of Microsoft.Net. At this this point, the API coverage is limited to .Net 1.1 with limited support for 2.0.
So why care? If you want your application to be a bit more platform agnostic. Linux, Windows, Unix, it is will work.
Will your application run under Mono? Good question, Phillip Haack has an article about Mono and migrating to it. The tool analyzes your source code and identifies issues that may prevent you from running on Mono.