DC Stands for Difficulty Class, and it represents the difficulty in either resisting, avoiding, or succumbing to the effects of a spell. When a spell lists in its descriptions that it requires a "Reflex Save for half" or a "Fort Negates" it means that a Save against the Spells DC must be rolled to avoid the effects of the spell.
In the case of "Reflex Halves" if a character succeeds in a reflex save against the Spell DC, he takes half damage from the spell effects as he's able to avoid the explosion, only get hit by part of the lightning bolt, etc.
If the case is "Fort Negates" it means that the effects of the spell are negated by a successful Fortitude save against the Spell DC. Spells like Poison have effects which you must shrug off with your body instead of your feet.
To calculate your Spell DC use the following Formula:
Spell DC = 10 + Spell Level + Primary Casting modifier ( INT for Psions and Wizards, CHA for Sorcerer's and Bards, WIS for Druids and Clerics )
An interesting thing to note is that you can use the feat Heighten Spell to prepare a spell in a higher level spell slot, which will in turn Increase the Spell DC. For example, with a spell like Glitterdust which is a second level spell, you could prepare it as a 5th level spell to increase the spell DC to make the effects harder to resist.
Alongside spells are also Spell-like abilities which have the (Ex) denoting Extraordinary abilities, or (Su) which indicates a supernatural ability.
The formula for the DC of those spells is slightly different, and is calculated with your level instead of the spells level.
Ex / Su Ability DC = 10 + 1/2 Level + Specified Ability Modifier ( For clerics Channel energy, this is CHA )
The Specified ability modifier can often be found in the ability description of the ability, such as the one for Channel Energy.