Basically, explosives will push the rock in the easiest direction.
As described, presumably they lay out the grid of holes and fill them, also as described, with explosive. The detonators (blasting caps) are timed so the holes nearest the open space (cliff face, previously excavated, whatever) go first. They will blow the rock in the direction of least resistance, toward the open air. Then next row go off, and since they are now near the surface, they throw the rock between them and the previous set of holes toward open space, and so on.
I had the opportunity for a short time to practice drilling for tunneling. the concept is similar, but requires a different pattern.
First, three large holes (say, 4 inch diameter) were drilled in a pattern of a triangle about a foot on a side, maybe up to 10 feet deep.
Then a spiral of approximately 1-inch holes is drilled in a circular patter, about 1 foot spacing or so, (all holes parallel, 10 feet deep.)
The holes are then loaded with explosive - first the blasting cap pushed all the way in with a length of wooden rod.
Then air spray will blow and compact the ANFO into the hole.
The blasting caps (at one time burnable, later electric) are connected in a sequence such that the ones around the big hole blow first.
A blasting cap is usually sufficient to set off the ANFO.
When the blast goes off, the first set of blasts break the rock around the initial 3 big holes.
Since the blasting cap is deep at the end, the blast wave travels from back to front, sending the rock outward from the drilling face.
Each successive blast pushes more rock outward.
When the blasts have finished, go in and clean up, pry away loose rock, screen to prevent falling rock, etc.
Often the tunnel is finished with a spray of concrete slurry over the screen.
Note that explosives are not magic. Like any other pressure, they will work in the easiest direction. They don’t necessarily crumble rock if the pressure wave has nowhere to go. They crack where the hammer of the pressure wave deforms the rock, typically where there is less resistance to movement - ie. the open side. I have seen occasional failures of the blasting which means parts of the frozen rock face had to be re-drilled and re-blasted. What is actually happening where you see the drillholes is that the pressure was far easier to relieve by pushing the rock on the open side of the cut. (Somewhat similar to when you brace yourself against a wall to push a load. the load moves before the wall, you hope.)
Of course, limestone is a lot softer and there are modern drill techniques where they drill and then hammer a hydraulic wedge into the hole and split off rock without explosives. This is simpler because they don’t have to exercise as much caution, and pull everyone out of the area, block traffic, etc.
Shaped charges? Think of them as a sledgehammer. An engineer described a very simple technique to me… shaped charges bought commercially were very expensive. Instead, they went to the local hardware store and bought a bunch of plastic funnels. they put the blasting cap in the spout and filled the cone with putty explosive (essentially like ANFO but a playdough consistency). When they ran across a boulder too big for the equipment, they put one of these onto it and set it off. Obviously, it is explosive and you don’t want to stand nearby - but the main pressure wave follows a conical path spreading out from the apex of the funnel toward the flat end. The result is a sledgehammer. the first time they tested it, the guy told me the boulder was intact - until the loader tapped it with the bucket and it crumbled into gravel. Very effective.