A smartcard is a card with an embedded chip that may store cryptographic keys and/or perform cryptographic functions. Smartcards are often use as employee ID badges or in contactless credit/debit cards.
Smartcards used for cryptographic functions such as identity verification, signing, and decryption are usually designed so that the cards can generate their own cryptographic public/private key pairs, such that the private key cannot be removed or exported from the card. Using a smartcard to decrypt or sign a piece of data is usually protected by a PIN or passcode.
If you receive a message, whose signature can be validated using the public key, then you know that the message could only have been signed using the private key stored on the smartcard, which means that the message came from someone having physical possession of the smartcard and who knows the PIN or passcode required to use the smartcard. Having the decryption key on the card directly enforces, that without card and PIN knowledge just the encrypted message is available.
SIM cards used in mobile phones are also smart cards, proving an existing account towards network and storing phone numbers and text messages.
EMV cards (also known as "chip and pin") use smartcards to increase security and decrease fraud. The EMV standard, and its test cases, are governed by EMVCo.
Smartcards have a dedicated standard: ISO/IEC 7816 that describes what defines a smartcard from physical characteristics to cryptographic information application, including protocols and commands.
Contactless smart card (such as PayPass and payWave etc) are covered by ISO/IEC 14443; that describe the physical characteristics of the card, power and signal interfaces, transmission and collision detection, and transmission protocols.
EMV cards are also issued with "dual" interfaces that use the same chip on the card and two external interfaces.
