Although the links (difflist, for-a-few-monads-more) that you posted are very interesting in their own right, you only need to understand the following in order to comprehend "shows" and "ShowS"...
* Partial Application
* Function Composition
Type Classes
==========
There are many references for understanding how these work, but the "shows" function simply depends on its first parameter being able to be shown through the use of the "Show" type-class.
Type Synonyms
============
Any type can have an "alias" created in the form of a type-synonym. Although these can be parameterised, in the case of "ShowS" it is not:
`type ShowS = String -> String`
This means that wherever you see a reference to "ShowS" in a type, you may replace it with "String -> String".
Partial application
=============
Look at a reference implementation of "shows" that Shrivats has described:
`shows x s = show x ++ s`
The type signature of "shows" focuses on the partially applied viewpoint, because (thanks to the type-synonym) it is written as if it only takes one argument:
`shows :: Show a => a -> ShowS`
However, with the "ShowS" synonym resolved, you can see that it actually takes two:
`shows :: Show a => a -> String -> String`
Keep in mind that although Shrivats implementation is semantically equivalent to the one in GHC.List, the performance characteristics may be different.
Function Composition
================
Although this isn't strictly required in order to understand "shows", it provides a potential motivation for why the function exists.
If you wished to chain together a bunch of String representations of various objects, leaving the possibility of adding more later, you would have to use many lambdas if you wished to constrain yourself to using "show" and "++". For example:
`showWithMore a = \x -> show a ++ x`
Applying these would become tedious:
`myBools = \x -> showWithMore True (showWithMore False x)`
Thankfully, this can be avoided through the use of function-composition:
``myBools = shows True . shows False`
Hopefully this goes some way to getting you to the core of the construction and motivation of these functions and synonyms.
As always, for a true understanding of the motivations behind such a function, nothing beats looking at the source code [1].