of "Virtual Studio Technology
VST is a "semi-open" standard for music software including support for digital recording, MIDI, EQs, effects, mixing, and automation. It is developed by Steinberg and was first seen in their Cubase line of studio software.
The way you usually see VST used today is in the form of plugins based on the VST API. Examples of such plugins can be filters, effects, GUI for controlling external MIDI instuments or software synths and samplers. Any VST-enabled sequencer or studio system can use these plugins and connect them.
VST was originally only used in Steinberg's own products, but have gained popularity and several VST-compatible products have appeared on the market recently. Until recently it seemed like VST would be the industry standard for DSP plugins but the appearance of DirectX-plugins have changed the picture somewhat.