Traditionally, the old Xian indicates the inner city inside of the old City Wall, where there are no high buildings and always the old houses and markets, shopping mall etc.
The new Xian indicates the Xiaozhai area where there are high buildings and modern constructions.
When you travel to Xian in China, it is a must to visit the old City Wall and Muslim Quarter that are situated in the old city. But it is quite interesting to explore the new city to see the contrast in Xian.