What does the number on the visual studio solution icon represent?

The numbers correspond to the internal version numbers of various editions of Visual Studio

http://en.wikipedia.org/wiki/Microsoft_Visual_Studio#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
Visual Studio 2017 = version 15
Visual Studio 2019 = version 16

The number on the icon indicates the version that the project or solution is compatible with.

It's what version of Visual Studio the solution was created with. 10 is for Visual Studio 2010, 9 is for Visual Studio 2008, 8 was for 2005, and 7 was for 2003. You might seen an 8 sometimes with VS 2008 if you set it to target .Net 2.0 features only, but that usually means you found an older solution file somewhere.