If you have an iPhone 5S or later, the phone measures your activity during the day automatically. Activity is your amount of steps since your last sleep session.
Right now, Sleep Cycle reads the number of steps from the device Sleep Cycle is installed on. We're not reading steps from Health app. We're working on reading the steps from Health app which means that it also will count the steps you're taking with your Apple Watch or other devices connected to the Health app.
You do not have to keep the app running to measure steps, the phone does this automatically. If you do not want the phone to measure this please go to:
iOS Settings -> Privacy -> Motion Activity