Pottery was made by coiling strands of clay mixed with a temper, usually sand or crushed rock. Temper was added to the clay to hold it together. Both the Anasazi and Fremont made excellent pottery and some of it was decorated with white slips and black paints. The Paiute and Shoshone made pottery in historic times. The archaeological record tells of murder, beatings, and possibly of cannibalism.
Nobody knows exactly what they mean.
Symbols have meanings, but the meaning can be different for each person that looks at them. Obviously, some symbols represent humans or animals but most of the time the real meaning is unknown. Petroglyphs are symbols pecked into the rock. Pictographs are actually painted on the rock. In Utah, we have both types of rock art.