I'm not sure "constructions" are the correct word. Buffalo jumps were generally natural cliffs and the heard was chased over them. The animals were corralled towards the jump by people on foot and by lighting fires, one of the few things that would make buffalo run rather than stand their ground. (Remember, no horses at this time)

They also included a runup where stone walls were built to corral the buffalo into a narrow point so they all ran off the cliff in roughly the same place. Without the walls the herd would turn unpredictably and avoid the cliff face.