What is core in processor?

The "core" in a processor is the microprocessor inside of the CPU(Central Processing Unit).

For example, if you have a Dual Core CPU then you have 2 microprocessors inside of the CPU, this allows you to do two things at once, as a microprocessor can only do one thing at a time the only exception to this is Multi-Threading which allows one core to do the work of multiple cores, but its not as fast as having multiple cores.