The pressure rises above the least principal stress and the rock splits. Proppant is placed so the crack stays conductive after the pumps stop. In a carbonate, acid can etch the faces instead, so the fracture stays open without a pack of grains. The fracture bypasses near-well damage and adds contact area in low-permeability rock.
It opens against the minimum horizontal stress in the usual stress regime, so the treating pressure is a stress measurement as well as a completion. A fracture that grows out of the pay into water or gas is a completion failure even if the pump schedule was followed. The word 'frac' in a drilling report can also mean a formation breakdown, which is a loss event, not a planned stimulation.