Some of the most powerful tools against vampires have their roots in Christian religion.
There are many reasons why this could be. The one I believe is that perhaps in the age when demons ruled, and humans just started to appear, the humans decided to cast a spell which would protect them from vampires. The cross may have been chosen as a symbol that would burn vampires. This could be a reason why churches would later use the symbol. I'm sure that back in the old days, certain people could cast such spells. Powerful witches and other humans with knowledge of spells would have been needed to rid the world of demons as the supreme race.
To make a cross become a symbol that would burn a vampire, I am sure that a spell would have to be cast on it, it would have to be blessed, or at least have some holy link. Otherwise, vampires would be burned by many things, like train tracks, or anything which has one long rectangle placed over another. The same thing applies for holy water. Regular water will not burn a vampire. The water must be blessed.
What exactly does a cross or holy water do? Well, crosses seem to have the same effect as fire does to a human. If a cross is held out to a vampire, they will back off. If strong (or crazy) enough, a vampire can touch a cross, just like a human can touch fire. Holy water is a lot like a cross, except if ingested, it will kill the vampire. Probably the water burns the insides of a vampire, eventually reaching the heart. Maybe if a cross is pushed up against a vampire's bare heart, it would kill them.
A bible also seems to act in the same way a cross does.
All three items act almost exactly the same, probably do the exact same thing (which is what leads me to belive that if a cross or bible touches a vampire's heart, it would kill them.) Some people think that anything can be blessed in the same way water is. I am not sure about this however.