The below is based on my current understanding. Please feel free to point out any errors or share any differing opinions.

VST = Virtual Studio Technology

In short, VST is an interface specification and SDK released by Steinberg (makers of Cubase) in 1996. VST Plugins are virtual instruments and effects developed with the VST SDK that are capable of integrating with a host software via the VST interface specification. It alls sounds very technical but put simply it enables you to expand the functionality of your host software (often a DAW) by loading plugins representing effects and virtual instruments. You can then virtually route a sound signal through those plugins. VST plugins are usually categorized into the following three groups:

• VST Instruments such as emulations of synthesizers. Sometimes shortened to VSTi.
• VST Effects such as reverb and flanger. The host software will often allow for effects to be chained.
• VST MIDI Effects. MIDI effects operate on MIDI signals (duh?) and those allow you to change pitch, repeat or add arpaggio to an incoming MIDI signal before routing it on to other plugins.

AU = Audio Unit

In short, AU is an Apple specific standard built on top of Core Audio. It is exposed to developers via a set of APIs provided by Mac OS X. It is essentially intended to provide the same functionality as the VST standard while providing lower latency and overall higher performance due to the fact that it is built directly on top of Core Audio by Apple Inc. However, due to the limited market reach of pure AU plugins, most developers and manufacturers do not provide dedicated AU plugins, instead they use commercial wrapper technologies such as Sonic Charge’s Symbiosis to add an AU compatibility layer on top of a VST plugin. Thus in my own (yes extremely limited) personal experience, you should always opt for the VST over the AU version of a plugin if both exist.