From Wikipedia: "Spelled alternatively as Sgwd Gwladys, the falls are formed where the Afon Pyrddin drops 20 ft (6 m) over a lip of the 'Twelve Foot Sandstone'. The native Welsh name was anglicized to Lady's Falls prior to 1900 due perhaps to the likeness of the name's pronunciation[4] but Gwladus is nevertheless a proper name, that of one of the many daughters of Brychan, the 5th-century King of Brycheinog. The sandstone tilts gently to the south so forcing the waters of the Pyrddin up against the foot of a high cliff of mudstone and over the left-hand side of the rock lip (when viewed from below). In higher water conditions the fall gradually extends further to the right. The upper surface of the sandstone is roughly patterned with the fossil roots of trees. A rocking stone (now dislodged) sits on this bench some 50 metres (160 ft) north of the falls."
There are two pubs a bistro and a carpark in Pontneddfechan, its about a 30 minute walk from there along a wonderfull trail through what is sometimes called the 'Celtic Rainforest' learn about the 'Fairwell rock' gunpowder and an errant Monk who escaped a monestry to live with the fairy people. Beyond Sqwd Gwladys to the north there is a series of smaller falls before the river emerges from being underground for 250 meters. Sqwd Gwladys is great place for picnics and is safe to swim in the summer. Beware/marvel at 'tombstoners' and take your rubish home.