"Traditional" or Trad climbing is climbing without any pre-placed gear, whether bolts, staples, pegs, pitons or RURPs (wot be RURPS? - Ed).
The idea is that you move up the rock using only hands and feet, and that any fall is arrested by a temporary piece of gear, usually a nut or a camming device.
Trad climbing is ubiquitous in Ireland, prevalent in the UK and a minority pursuit almost anywhere else. This is because bolted climbing (where falls are arrested by a bolt drilled into the rock semi-permanantly) has become the norm in many countries. Bolts remove a lot (but not all) the danger, and require less skill from the leader.