"Trad", as in "traditional", can also be in reference to "trad rock". While the abbreviation refers to the same original word as in ryano's writeup, there is a distinctive difference between trad rock and traditional irish folk music (in addition to some passing similarities).

Kristin Sage Rockermann (her real name? Gods only know) transcribed the following from a conversation she had at a trad convention in a Pitchfork Media review:

"Trad-rock is... well... it's not really Britpop. But you know trad bands... like the Chieftains-- they play traditional music. So, trad-rock is really traditional rock and roll." To clarify, I ask him, "So, you guys are into the Stones and Led Zeppelin?" He laughs a knowing laugh and replies slowly, "Don't you see? We're living in a post-Oasis world."

So, what is trad rock? Perhaps Oasis, Travis, and arguably even Coldplay and the like. In trad you would most commonly hear acoustic or clean guitars and electric bass alongside reverb-soaked percussion (tambourines?) and vocals. It's a loose categorical divison of rock that in many places, the U.S. among them, people have not yet begun to make. Then again, most people in the US have never heard of the Smiths.