Authentication is the process in which credentials are cross-referenced with those in a database of authorized users. In order to be given access, the credentials must match those in the database. The difference between single-factor and two-factor authentication is simple — how many factors are used in the verification process. In single-factor authentication, only a single factor (i.e. typing in a username and password) is used. By contrast, two-factor authentication utilizes something you know (such as a password) and something you have (such a USB token) to create a secure connection between you and the system you are logging into.
If fraudsters were able to steal your password, they would need to have also stolen your USB token before they could access your data. One of the most common examples of multi-factor authentication occurs at an ATM, where users are required to enter a PIN (something they know) and a card (something they have).