In non-uniform circular motion, we have a centripetal acceleration from the circular part and a tangential component. The net acceleration is the vector sum of these two accelerations.
For example in the previous page "Check your understanding questions". Speeding in a CCW motion yielded an acceleration that points down and to the left if you are at the top.
Look at example 8.6 and problem solving strategy 8.1 on p 195.
At the end of the day we are simply using F=ma in the rtz directions.
An excellent example of non-uniform circular motion is the pendulum.