As you know (or maybe you don't) the basic principle of optical discs such as CDs and DVDs is to read pits on the discs surface (actually I think that technically they measure transitions from pits to flats, but I could be wrong about that). Anyhow, this is done by shining a laser on a surface and detecting the amount of light reflected using a photocell. By altering the CD surface so that the reflectivity changes between a pit and a flat, you the encode 0s and 1s that make up your data.
So, to answer your question, the DVD format specifies a red laser as opposed to the infrared laser used for CDs. Since the red laser has a shorter wavelength than the infrared laser, it can be used to distinguish smaller features. This means that you can make shorter pits and pack them more tightly together. Obviously by packing things more closely together, you can store more information on the same area and this is why DVDs can hold more information than CDs.
I've skipped over a lot of the details, but this is the gist of it. There's also a specification for dual layers on DVD that didn't exist for CDs to further enhance capacity. Finally, the next generation formats such as Blu-Ray and HD-DVD make use of blue lasers that have an even smaller wavelength that can be used to distinguish even smaller features.
There's a more detailed explanation here if you'd like to read more:
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