its kind of like wearing armor all made by the same craftsmen. It tends to fit together better and thus give more benefit.
The one example i know if is the Defias set. It constitutes 5 pieces (Chest, legs, belt, boots, and gloves). The more pieces of a set you have and wear, the more of a bonus you get (I have the defias chest and defias belt, i get a +10 armor bonus on top of the armor/stats from the 2 pieces). You can tell that you have a piece of set armor because it'll say something to that effect in the armors description, and tell you what other pieces there are. Along with the ones you currently are wearing, and need in order to complete the set.
Go to the AH and just type in Defias with the leather armor section selected and you should see at least one piece of it up for sale. Just looking at the description ought to give you a better idea then what i can explain in words.