There are two copper contacts that conduct battery current to the motor through the plunger solenoid. These wear out with time and should be replace around 100-120K miles depending how many start cycles. When you hear a loud click and, because of wear, no current flows these are it.
See:
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For quite a while I would hit the old starter with a rubber hammer to get it
> to stop CLICKing, instead of starting.
>
> When that stopped working so well, I had a new starter installed. It was
> fine for a week, and then intermittently started CLICKing when I tried to
> start the car.
>
> I next installed a brand new Die Hard Gold battery, which is a giant
> overkill of that car's needs: Now it's CLICKing again anyway...
>
> Every once in a while it clicks, and today, in weather over 95 degrees, it
> took me ten minutes to get it to work, hitting it with a rubber hammer and
> pouring cold water over it. Then later today it took 20 minutes to get the
> thing to start.
>
> What is going on?
>
> There are those wires leading up to the battery, alternator, and the
> starter, which have what look like fuses in plastic cases. Could that be a
> place to start?
>
> What does it require to start a car besides a battery and a starter? >
> ---firefly