"DR 10/silver and magic" means that WEAPONS
(including natural weapons, unarmed strikes, and improvised weapons) used against the vampire deal 10 points less damage unless those weapons are made of silver
(or coated in alchemical silver or a silversheen elixir, as described in the 3.5 PH or DMG, I forget which) AND also possess a magical enhancement bonus to attack
(whether it is a magic weapon normally, or just received a temporary enhancement bonus from a magical source, such as a Magic Weapon or Magic Fang spell).
Spells, energy effects (including things like lava, acid pools, cold damage from freezing water, alchemist's fire, the Shocking ability of some magic weapons, and so on), spell-like effects (including psionic powers), and supernatural effects, all ignore Damage Reduction. So a vampire can be thrown into a furnace and WILL burn just as easily as a human would, though he'll probably be ticked off when he flies out of the flames and comes to kill the offending adventurer.
DR with a special material in its description, such as the "silver" in a vampire's DR, DOES NOT confer the creature to bypass that same DR type. So vampires cannot hurt each other very effectively with natural weapons; they'll be dealing 10 less damage to each other because of their Damage Reduction. Likewise with regards to werewolves; they deal pitiful damage to one another in unarmed combat with tooth and claw, because werewolves' DR is only bypassed by silver (when making physical attacks; as noted already, energy and spells and such always bypass DR). A magic weapon wouldn't hurt werewolves or vampires as well as it would hurt humans, unless that magic weapon were also silvered.
However, a vampire's natural weapons are considered to be magically enhanced for purposes of overcoming Damage Reduction; DR X/magic (or DR X/some-material-or-alignment and magic) confers that minor benefit upon the creature's own natural weapons.
Here's a link to the D20 Hypertext SRD's entry on Damage Reduction, for a more complete description.
http://www.d20srd.org/srd/specialAbilities.htm#damageReduction