A function is cyclical if it repeats over and over in a predictable way.
The population of your school's graduating class may increase and decrease over time.
What kind of graph would best show this information?
This would be modeled best with a step graph.
Are you hungry and not hungry at the same times each day?
This may or may not be periodic.
The high and low tide graph is approximately periodic over short periods of time.
Do a Google search for 'tide graph images' to see for yourself.