What is the Secure Element in Apple Pay?

GlobalPlatform defines the Secure Element as a "tamper-resistant platform (typically a one chip secure microcontroller) capable of securely hosting applications and their confidential and cryptographic data (e.g. key management) in accordance with the rules and security requirements set forth by a set of well-identified trusted authorities."

In the iPhone 6, 6 Plus and Apple Watch, the Secure Element is embedded into the NFC chip, which is used by Apple Pay at payment terminals. The NFC chip facilitates communication between the terminal and the Secure Element. Software on the SE emulates your card and provides a secure storage and execution environment for the payment application.

See here for more information about Apple Pay security.