Answers:
An example of an arc length could be running around a circular track. An arc is the distance along the outside of a circle. When people run around a circular track, they are running around an arc. You could calculate the distance of the arc to see how far someone ran.
An example of a sector area could be the area covered by a lawn sprinkler rotating around a fixed point. A sprinkler that moves around in a circle is spraying water in the shape of a sector of a circle.