Build Solution - Builds any assemblies which have changed files. If an assembly has no changes, it won't be re-built. Also will not delete any intermediate files.
Used most commonly.
Rebuild Solution - Rebuilds all assemblies regardless of changes but leaves intermediate files.
Used when you notice that Visual Studio didn't incorporate your changes in the latest assembly. Sometimes Visual Studio does make mistakes.
Clean Solution - Delete all intermediate files.
Used when all else fails and you need to clean everything up and start fresh.