The short answer is that the i3 is in fact a dual core processor, but with more features than the previous generation of dual core processors (Intel Core Duo.)
The Intel i3 processor has a faster bus speed and more cache memory than an Intel Core Duo processor. It also has integrated graphics.
For those of you building your own computer, you can buy an i3 processor and a motherboard with an integrated HDMI output. This means that you don't have to buy your own video card.
Caveat: In the i3/i5/i7 line of processors, if you get a quad-core processor (like the i5-760) the trade-off is that it does not have the integrated graphics, and so you should not get a motherboard that has the on-board video outputs.
Source can be found in the link posted in Sources and related links below.
I rightly enjoy this answer above, but would like to add that all i3, i5, and i7 Intel processers possess integrated graphics solutions after Lynnfield. This means Sandy Bridge, Ivy Bridge, and Haswell. This means if the i3, i5, or i7 has a 4 digit number instead of 3 digit number for reference, it will support integrated graphics. An i5-760 has no integrated video, but an i5-2500k does.
Core 2 Duo uses a different socket than all iterations of the i3 processor, which is important to note if a consumer is interest in upgrading / changing from Duo to i3.