That's a function definition -- a and b are the arguments. Caml has a funny syntax. Here's an annotated version, with comments (* like this *). 

 
module StringCmp =
  struct
    type t = string (* This is like a C typedef *)

    (* This is a function definition. 'let compare a b = <foo>'
       declares a function that takes two arguments a and b. The <foo>
       expression after the = is the function body. Function calls don't
       use the 'f(x, y)' syntax.  Instead, Caml uses simple
       juxtaposition: 'f x y' instead. *)

    let compare a b =
      compare (String.lowercase a) (String.lowercase b)

    (* This call to compare calls the generic comparison function, and
       rebinds it locally in this module. (String.lowercase s) will return
       a lowercase version. So what we are doing is lowercasing both args
       and then calling the generic compare, to get a case-insensitive 
       comparison. 
    *)
  end