HD DVD is the "next generation DVD" and has been standardized by the DVD Forum as its official "next generation" format.
Originally, the first "next gen format" to gain wide industry support was Blu-Ray, which was developed by Sony and Philips. However, due variety of reasons, Toshiba and NEC decided to bring their own format to the table, causing a similar situation to the next generation video format as the DVD-R and DVD+R caused to the recordable DVD media.
Anyway, HD-DVD is supported heavily by large companies such as Microsoft, but it still remains to be seen whether the format can have equal footing alongside Blu-ray.
HD-DVD uses blue-laser technology (just like Blu-ray does, opposed to DVD's red laser) and can fit approximately 15 gigabytes to one disc layer (compared to appx. 4.3 gigabytes on one DVD disc's layer).
HD-DVD's officially supported video and audio codecs aren't decided yet (late summer, 2005), but currently approved are the traditional MPEG-2, the high-quality MPEG-4 AVC and Microsoft's VC-1.
HD-DVD's maximum supported screen resolution according to its original specs was 1080i as opposed to Blu-ray's 1080p. This has been changed in later tech spec revisions, but early HD DVD players are limited to 1080i.