Apple has (finally) created a dedicated app for tracking your period, called Cycle Tracking. The new app isn't available quite yet -- but you'll be able to use it later this year when and are available to the public. It is a standalone app on the Apple Watch ($384 at Amazon) and is built into the on the iPhone ($1,000 at Amazon).
Tracking your menstrual cycle is an important way to keep tabs on your health. Knowing when your next cycle starts not only helps you always be prepared, it's also useful if you are trying to conceive, or are living with conditions like polycystic ovarian syndrome (PCOS) and endometriosis.
During your period you can log your flow level and symptoms like cramps or headaches in the Cycle Tracking app. As you log information about your cycle, the app will predict when your next period will begin and when you're ovulating, and then generate notifications on your iPhone and/or Apple Watch.
You can also log fertility stats like basal body temperature or the results from an ovulation test. The app uses that information to create a fertility window -- the few days each month when you're most likely to get pregnant. You can see an overview of your cycle in the Apple Health iPhone app, and you can log symptoms directly from your Apple Watch.
Apple's Cycle Tracking follows a model very similar to other menstruation-tracking apps such as Clue and Eve, both of which use the data you enter to predict when your period will arrive and when you're ovulating.