Authentication is the process of identifying an individual based on a username and a password. Authentication is similar to authorization since it allows an individual access to system objects based on their identity (username and password). Authentication basically ensures that in user is who he/she says they are.
A password is a secret series of characters, letters, and numbers that allows a user to access a computer, files, and even programs. A password ensures that unauthorized users do not have access to those files, computers, etc... Ideally, a password should be something that no one could guess. It should be something that we can remember, while no one we know could figure it out. Using numbers, characters and capitalized letters will make the password more difficult to figure out, which will make access to computers, and files more difficult for hackers to access and you will be better protected.
A smart card is a plastic card. Similar to the size of a credit card, it has an embedded microchip that can be loaded with information. It is used from phone cards (sim cards), to credit cards as well as other applications, and data can be refreshed anytime.
A smart card contains more information than a card with only a magnetic strip and can also be programmed for different purposes. A smart card is much safer than a magnetic strip, and are very popular in Europe (they are on every debit/credit cards).
Biometrics refers to the technology using body characteristics such as fingerprints, DNA, eye retina/iris, facial patterns, for authentification purposes. It is used increasingly within companies for security purposes, as well as green cards (US permanent resident cards) where fingerprints are being used as well as a picture. Biometric data is usually encrypted and to be identified, certain data points need to match the data saved.