How does slice category help create functor? Reading Awodey [p.16-17], he states the following:

The slice category $\boldsymbol{C}/C$ of a cateogry $\boldsymbol{C}$ over an object $C\in\boldsymbol{C}$ has [definition of slice category follows] (...)
  If $g: C\to D$ is any arrow, then there is a composition functor,
  $g_{*}: \boldsymbol{C}/C \to \boldsymbol{C}/D$
  defined by $g_{*}(f) = g\circ f$, and similarly for arrows in $\boldsymbol{C}/C$.
  Indeed, the whole construction is a functor,
       $\boldsymbol{C}/(-): \boldsymbol{C} \to \boldsymbol{\operatorname{Cat}}$ as the reader can easily verify.

So I have a few questions:


*

*What does the $(-)$ symbol mean?

*What does the author mean by the expression "the whole construction"?

*And how is that "construction" a functor? To my best understanding slice category was a "category" and not a functor.


P.S.: Please let me know if it's not clear, and I'll expand/clarify.
P.S.S.: My mathematics level: newbie 
 A: $\boldsymbol{C}/(-)$ is category theory notation jargon for the mapping which takes an object $X$ from $|\boldsymbol{C}|$ and yields the slice category $\boldsymbol{C}/X$.
Since slice category is a category, it can be thought of as an object in   $\boldsymbol{Cat}$, which is the category whose objects are categories. So the mapping $\boldsymbol{C}/(-)$ takes objects in category $\boldsymbol{C}$ and yields objects in category $\boldsymbol{Cat}$.
Together with the corresponding mapping of arrows that takes an arrow $g$ (from category $\boldsymbol{C}$) and yields the arrow  $g_*$ (from category $\boldsymbol{Cat}$), the mapping $\boldsymbol{C}/(-)$ forms a functor from $\boldsymbol{C}$ to $\boldsymbol{Cat}$. It has the necessary ingredients: a mapping between the objects of two categories (namely $\boldsymbol{C}$ and $\boldsymbol{Cat}$) and a mapping between the arrows of those categories.
(You should now verify that these mappings do in fact form a functor: They must respect sources and targets of arrows, and identities and compositions.)
By "the whole construction is a functor", Awodey means "the slice construction (for objects), together with the $g_*$ construction I just described (for arrows) is a functor."
The "$(-)$" notation is common in category theory; for some reason they don't use the $\mapsto$ notation that one would expect.  The mapping that turns $g$ into $g_*$ might be written as $(-)_*$.
