A multi-core CPU is a kind of CPU that has two or more actual chips inside it (known as cores). This allows a computer to actually be processing multiple things at once and is often seen as the solution to continuing Moore's law.
From Wikipedia's entry:
A multi-core processor is a single computing component with two or more independent actual processors (called "cores"), which are the units that read and execute program instructions.1 The data in the instruction tells the processor what to do. The instructions are very basic things like reading data from memory or sending data to the user display, but they are processed so rapidly that we experience the results as the smooth operation of a program. Manufacturers typically integrate the cores onto a single integrated circuit die (known as a chip multiprocessor or CMP), or onto multiple dies in a single chip package.
A multi-core processor implements multiprocessing in a single physical package. Designers may couple cores in a multi-core device tightly or loosely. For example, cores may or may not share caches, and they may implement message passing or shared memory inter-core communication methods. Common network topologies to interconnect cores include bus, ring, two-dimensional mesh, and crossbar. Homogeneous multi-core systems include only identical cores, heterogeneous multi-core systems have cores which are not identical. Just as with single-processor systems, cores in multi-core systems may implement architectures such as superscalar, VLIW, vector processing, SIMD, or multithreading.