How can the D3 external computer DAC improve my music?

The D3 is essentially a very high end external sound card. Its components and implementation make it more capable than what might be built in to a computer, not to mention the benefit of moving those sensitive components external to the potentially noisy interior of your computer. All of this means the signal your speakers receive will be clearer, with a lower noise-floor, and with a more pronounced dynamic range over your internal sound card.