In the following diagram, we see that we can get from A to C by way of the g o f composition.
From C, we can get to D using the h arrow, which we can write as ho(gof).
Note that this is the same as h(f(g)). This notation seems more intuitive than using the composition operation, but they mean the same thing.
From the following diagram, we see that ho(gof) is the same as (hog)of.
So, our category obeys the law of associativity. The next diagram is another illustration of the associativity of composition:
That diagram says ...
