How can the DAC3 external computer DAC improve my music?

The DAC3 is essentially a very high-end external sound card. Its components and implementation of those components make it more capable than what might be built into a computer, not to mention the benefit of moving those sensitive components outside and away from the potentially noisy interior of your computer. All of this means the signal your speakers or wired headphones receive will be clearer, with a lower noise-floor, and with a more pronounced dynamic range over your internal sound card.