Why do we use a diac for triggering a triac?
See http://en.wikipedia.org/wiki/DIAC for a diagram of the breakdown behaviour of a Diac.

As you can see there, a Diac is non conductive up to a certain breakdown voltage, above it becomes conductive, until the current drops below a threshold value.

In short, the diac is forming the pulse that is needed to trigger the triac.