So the brushes in a commutator are fixed and assume a constant polarity, so how does the commutator reverse the direction of current?
So how does a commutator fit in? Just because we have two different
materials at all times against the brushes, how does that aid in
reversing the direction?

Commutator system (simplified): -

Link to picture. Link to lots of pictures in the search entitled: &quot;commutator brush current reversal&quot;.