The two cores are built onto one piece of silicon. That piece of silicon is in fact referred to as a "die" The old Pentium D dual cores had two separate dies on the chip itself, where as with the Core2 Duo, Intel created 1 die with two cores on it.
Think of it in terms of a standard sheet of paper. Draw a few rectangles on the paper. You can draw one, two, four or six, or eight, or as many as you can fit. The single sheet of paper could be analogous to the processor "die" which is a single piece of silicon, and the rectangles you drew on the paper could all be different processor cores within that die. Core2 Duo happens to have two cores drawn on its die.