Virtual Instruments take many forms but are generally either virtual synthesizers or samplers. They include software versions of real world instruments like pianos and guitars, and attempt to recreate the sound using either recorded samples, software based algorithms or a combination of both.
Virtual Instruments are usually run within your DAW (Digital Audio Workstation)/Sequencer as plug-ins as they require notes to sent via MIDI in order to output audio. However many have the ability to be run as standalone applications which is especially useful for live use.