AMD originally paved their way into the desktop CPU market by offering CPUs comparable to Intel's at a much better price point. That trend of offering low cost CPUs as a way to attracting more customers remained through all the way up to the Thoroughbred-based Athlons. In the past few years the trend changed, with AMD offering pricey “enthusiast” CPUs and the Celerons seeing very low price points, which played a part in how AMD lost their edge. A triple-core Phenom priced in nearly the same bracket as a Core 2 Duo might weigh heavily in their favor.
Intel does not have a triple-core competitor, as their design allows them to create only dual or quad core CPUs. AMD is betting that the cost to performance ratio of a triple core processor will help them.