Apple Pay is a digital wallet from Apple which lets you use a compatible iPhone, Apple Watch or iPad to make secure contactless purchase in stores, within selected apps and participating websites.
Other helpful FAQs.
Apple Pay works with iPhone 6 and later in stores, apps, and websites in Safari; with Apple Watch in stores and apps; with iPad Pro, iPad Air 2, and iPad mini 3 and later in apps and websites; and with Mac in Safari with an Apple Pay enabled iPhone 6 or later or Apple Watch. For a list of compatible Apple Pay devices, see https://support.apple.com/km207105
No, your card details are not stored on the device or in the Cloud. When a card is added to Apple Pay, a Device Account Number replaces the need for the card number.
The Device Account Number is used to make secure purchases in stores and within apps and websites. It will not work if it is compromised in any way and cannot be used outside of the device it is assigned to.
The Device Account Number can be found by opening the Wallet app and tapping the (i) symbol in the bottom right corner and then scrolling down to find Device Account Number.