Conglomerates are geological history writ large. More than any other stone they capture the vast eras of geological action. Because they are made up of rocks which have been deposited, altered to rock, eroded into rounded blocks or pebbles, moved and redeposited, then cemented together to make stone again, they contain a massive amount of information about an area. However, they also reminding us of our huge ignorance of much of geological history.
The conglomerate of Carn Gafallt formed in the Lower Silurian Period 'Llandovery' Epoch* (~444 to 428 Million years ago: Timeline), when most of mid-Wales was deep under the sea. Rocks eroded from the land built up in the shallows at the edge of the sea, then slid down in submarine channels in the continental shelf in giant avalanches. These rocks and pebbles mixed with mud and other deposits. This mixture built up and the pressure of layer upon layer of mud, followed by later material, slowly turned the mix at the bottom into the rock we see today. The older rock pebbles in this particular conglomerate are the hardest bits, so they tend to be easily released from the cement-like matrix around them, leaving hemispherical indents in the rock.
You can read about conglomerates here. There's no complete website on the geological history of Wales, but this good site can be supplemented with a local plate-tectonics history here, and this global picture of the Silurian.