it is clearer to write
let fn = f . g . h
let fn x = f (g (h x))
The term originated in topology, a branch of mathematics which works with spaces composed of points, and functions between those spaces. So a 'points-free' definition of a function is one which does not explicitly mention the points (values) of the space on which the function acts. In Haskell, our 'space' is some type, and 'points' are values.
Pros
This style is particularly useful when deriving efficient programs by calculation and, in general, constitutes good discipline. It helps the writer (and reader) think about composing functions (high level), rather than shuffling data (low level).
It is a common experience when rewriting expressions in pointfree style to derive more compact, clearer versions of the code -- explicit points often obscure the underlying algorithm.
Cons
Point-free style can (clearly) lead to Obfuscation when used unwisely. As higher-order functions are chained together, it can become harder to mentally infer the types of expressions. The mental cues to an expression's type (explicit function arguments, and the number of arguments) go missing.
Point-free style often times leads to code which is difficult to modify. A function written in a pointfree style may have to be radically changed to make minor changes in functionality. This is because the function becomes more complicated than a composition of lambdas and other functions, and compositions must be changed to application for a pointful function.
Perhaps these are why pointfree style is sometimes (often?) referred to as pointless style.
