The empty function is an inert function whose name is `` and so appears as empty (invisible). For example,

``(a);
                     (a)

It can be used to group quantities that would otherwise be combined by Maple.  It's primary use is in ifactor, where it prevents the terms from being recombined:

ifactor(6);
                     (2)*(3)

The @ symbol is used for function composition (it is the closest non-letter ascii symbol corresponding to the usual mathematical symbol for function composition, the open centered circle).  Thus

(f@g)(x)
                    f(g(x))

Similary, (``@denom)(x) is equivalent to ``(denom(x)), which visually encloses the denominator of x in parentheses. Somewhat more elaborate is

makefrac := (``@numer)/(``@denom):

This works (as described herein) because with Maple one can apply an algebraic expression to arguments, the arguments are then passed to each of the algebraic terms.  For example (f/g)(x) evaluates to f(x)/g(x).  So makefrac(x) evaluates to ``(numer(x))/``(denom(x)) which then displays the numerator and denominator of x as a fraction, with no automatic recombination (numer and denom are designed to give the appropriate answer even if their arguments are not of type `*`).