In the housing industry, DEMO is shorthand for DEMOLISH, the procedure used by renovators and construction workers to tear down that which is to be replaced in order to upgrade a property and increase its value
In the recording industry, DEMO is shorthand for DEMONSTRATION, the procedure used by artists, labels, producers, and songwriters to preview a song or musical project in order to choose what to record or continue to tweak before committing the time and money to realize a finished product or artistic statement.
There are other definitions of DEMO aside from these two, but when it comes to music, the definitions can oft-times be interchangeable …in, and out, of order.