The textbook answer is: A virtual machine (VM) is a software implementation of a machine (i.e. a computer) that executes programs like a physical machine.
The computers in the library with Trades software installed are virtual machines. All operating system files and software are installed on a server. What is seen on the screen of your "session" is taking place physically at another location. You are looking at a snapshot of this activity. Hence, no data can be stored "locally" on the machine in front of you.