The numbers correspond to the internal version numbers of various editions of Visual Studio
http://en.wikipedia.org/wiki/Microsoft_Visual_Studio#Version_history
Visual Studio 6.0 (1998)
Visual Studio .NET (2002) = version 7
Visual Studio .NET 2003 = version 7.1
Visual Studio 2005 = version 8
Visual Studio 2008 = version 9
Visual Studio 2010 = version 10
Visual Studio 2012 = version 11
Visual Studio 2013 = version 12
Visual Studio 2015 = version 14
The number on the icon indicates the version that the project or solution is compatible with.