Blue Ray won for a few decisive factors.
1) It's cheaper to produce than HD DVD. (Despite this they charge more)
2) It holds more data.
3) The most important for big business. It's much harder to illegally copy.
4) It's far more durable than DVD, CD, HD DVD. You can take a knife to Blue Ray, scratch it up and it'll still run.
5) Before Sony launched the format, they made exclusive deals with major distributors like Warner Brothers.
What doomed HD DVD is was too similar to Blue Ray. They didn't realize big business wants to maintain that monopoly. This is actually a disadvantage. It means higher prices because there's no competition.