Light Switch 3-wire but with 2 permanent lives
Use a 3-way wire connector of the type customary in your area to attach a pigtail (short piece of wire of the same gauge as the rest) to the two existing hot (live) wires, and then hook the pigtail up to the dimmer's common input.

Michael Karas' explanation is the most likely one, by the way -- it looks like whoever installed this switch was being a bit hackish or didn't have the extra wire connector and pigtail at hand, so they simply twisted the two wires together and stuffed them into the backstab common terminal on the switch.