The period of a periodical phenomenon is the length of the interval on which the graph repeats
You can choose which part you take for that.
You might take the part of a wave between one maximum and the next. But also from the first minimum to the next minimum. Or from an arbitrary point to the (LOOK OUT!) second point at the same height on the graph.
For the length of the interval on which the graph repeats itself, it does not matter which part of the graph you take. This length is always the same if the graph is truly periodical.
The period of the days of the week is equal to days.
For a turning wheel the period could be seconds.
Sometimes the period is called the wave length.
The number of periods per unit of time is called the frequency.