From LabVIEW Wiki
VI stands for Virtual Instrument, the basic building block of programs written in LabVIEW. It is similar to a function or subroutine in other programming languages. It includes the Front Panel (containing Controls and Indicators), the Block Diagram (containing Control Terminals, Wires, and Structures and various other GObject nodes), the VI's Icon and its Connector Pane (as well as compiled executable code which is hidden behind the scenes).
The term Virtual Instrument is a play off of the fact that LabVIEW applications are designed for writing software that simulates the functionality of instruments -- rather than being a physical instrument on a laboratory bench, they are virtual and exist in software.
LabVIEW VIs are saved as *.vi files in a proprietary binary format defined by National Instruments, the makers of LabVIEW.