Shaanxi, pronounced roughly "Shahn-shee", is a north-central province of China, and includes portions of the Loess Plateau on the middle reaches of the Yellow River as well as the Qinling Mountains across the southern part of the province.
Gansu is a province in the North West region of China. Historically, it is the combination of the two regions, gan and su, and marked the end or beginning of China proper depending upon if you were traveling east towards Xi'an or west towards Central Asia and Europe.
Ningxia is an autonomous region in North West China. Ningxia Hui Autonomous Region, established on October 25th, 1958, is bordered by Inner Mongolia to the north and west, Shaanxi to the east and Gansu to the south.