A processor with two cores. Much like the processor chip is the "brain" of a device, the core is the "brain" of the processor. Therefore a dual-core processor chip is like two processors on one chip.
A dual-core processor chip can often provide better performance than a traditional single-core processor, however it is not automatically twice as fast. Software - including the system OS and/or individual apps - must be specifically designed to split tasks among multiple cores in order to benefit and run faster.
Some dual-core chips provide better performance at the expense of battery life, compared to single-core chips. Other dual-core chips provide a battery life benefit by allowing one core to be turned off when it is not needed.