Basically it's choosing a new class that can be used in combination with your old one. You stop gaining experience in your base class and start gaining in your second class from 0 on. It is NOT multi-class. A multi-class character is two (or three) classes at the same time, and his experience is divided over those classes. If you decide to dual-class, your base class will become inactive. You won't be able to use its abilities any more until your second class supercedes it by one level. For example, the abilities of a level 5 mage dual-classed into a cleric will become available again when the second class, the cleric, reaches level 6. Keep in mind only HUMANS can dual-class and that dual-classing only allows you to choose two classes, never a third, unlike multi-classing. For the requirements and restrictions on dual-classing check parts 3 and 5.

These classes can NEVER dual-class:
paladin
bard
monk
barbarian
sorcerer

In order to dual-class you need to have a rating of at least 15 on the primary stat of your base class and a rating of 17 on the primary stat of your second class.

Here's a list of all the possible dual-classes and primary stats requirements:

Fighter/mage= 15 STR and 17 INT
Fighter/thief= 15 STR and 17 DEX
Fighter/cleric= 15 STR and 17 WIS
Fighter/druid= 15 STR, 17 WIS and 17 CHA (mind you only true neutral characters can dual-class into a druid)

Thief/mage= 15 DEX and 17 INT
Thief/fighter= 15 DEX and 17 STR
Thief/cleric= 15 DEX and 17 WIS

Mage/thief= 15 INT and 17 DEX
Mage/fighter= 15 INT and 17 STR
Mage/cleric= 15 INT and 17 WIS

Cleric/fighter= 15 WIS and 17 STR
Cleric/mage= 15 WIS and 17 INT
Cleric/thief= 15 WIS and 17 DEX
Cleric/ranger= 17 WIS, 17 STR and 17 DEX (only good alignments can choose to dual-class into a ranger)

Ranger/cleric= 15 STR, 15 DEX and 17 WIS

Druid/fighter= 15 WIS, 15 CHA and 17 STR