Let's start with the pendulum stationary at the top of its swing.
Gravity pulls down on the pendulum bob, and the cord pulls in - preventing itself being further stretched by the component of gravity acting along its length.
The resultant force (the "result" of adding these two) is at right angles to the cord, and the pendulum accelerates in this direction.
Once the pendulum is moving the cord does more than oppose the component of gravity along it; it also pulls the pendulum bob in to keep it on a circular path.
Splitting up the resultant force on the pendulum bob (into two magenta arrows) we can see it as a combination of one force pulling the pendulum in, and another accelerating it along its circular path.
When the pendulum reaches the bottom of its swing all forces are vertical (if friction is zero); gravity pulling down, and the greater cord tension pulling up. The resultant force is entirely the centripetal force needed to keep the pendulum on its circular path.
As the pendulum climbs the other side there is again a growing component of the resultant force along the pendulum's path. But now it acts to slow the pendulum down - until it hangs stationary for a moment at the top of its swing the other side.

Changes in tension
On a swing
Laws of Motion