What does "a category itself can be regarded as a sort of generalized monoid" mean? Categories for the Working Mathematicians says

the  fundamental  notion  of category  theory  is  that  of  a
  monoid - a set with a binary operation of multiplication that is
  associative  and  that  has  a  unit;  a  category  itself can  be 
  regarded  as  a  sort  of  generalized monoid. Chapters VI and VII
  explore this notion and its generalizations.

What does "a  category  itself can  be  regarded  as  a  sort  of  generalized monoid" mean?
Thanks.
 A: Per the passage itself, a more complete explanation will occur later in the text. That said:
The starting observation is that we can identify monoids with categories with one object. The intuitive direction is that for any category $D$ and any object $*\in Ob(D)$, the collection of morphisms $Hom(*,*)$ forms a monoid under composition. If $D$ has only a single object, this is the collection of all morphisms; thus, each one-object category gives us a monoid of morphisms.
The other direction may feel a bit slippery, but it's really no harder. Given a monoid $M$, we consider the one-object category $C_M$ with object $*$ and a morphism $f_m:*\rightarrow *$ for each $m\in M$, with the composition rule corresponding to multiplication in the monoid: $$f_m\circ f_n=f_{m\cdot n}.$$ Note that the object $*$ has absolutely no content - one of the themes of category theory is that it's the morphisms, not the objects themselves, that are actually important, and this is a great example of that.


*

*Incidentally, and very importantly, this correspondence also carries over to maps: homomorphisms between monoids correspond exactly to functors between the corresponding categories. 


Now what about an arbitrary category - that is, when we have multiple objects? Well, each object $*$ considered on its own has an attached monoid $Hom(*,*)$, as noted above, but we have additional structure present due to the morphisms between distinct objects. So a one-object category is a monoid (and indeed that's an exact correspondence), but an arbitrary category is somehow a bunch of monoids with some connections between them.

Along the same lines, groups correspond to one-object categories where every morphism is invertible (with group homomorphisms corresponding to functors between those), with "generalized groups" being arbitrary categories where all morphisms are invertible - these are called groupoids (warning: this clashes with earlier usage of the term).
We can also view other algebraic structures like rings as one-element categories with various properties or additional structure, but this gets more complicated.
