Arpeggiators are one of the most fun and “ancient” electronic music tools, and consist in editable algorithms that play the notes of a chord following a regular sequenced pattern. Like anything trendy in the 80s, arpeggiators are coming back in the early aughts with a vengeance. If you are not into their mechanical “feel”, you can try and use them to build textural background, using more than one of them in different stereo placements, or as random “melody generators”, if you slow them down a lot.
In the last few years most DAWs have introduced very useful simple Midi arpeggiators, which can apply this effect to any VST or midi instrument you own. But if you are looking for something a little more deep and involved, you should check out the 7 Aliens Catanya Arpeggiator VSTi plug in (pictured, 45 Euros), which features 1200 built-in ready to use patterns capable of transforming simple chords into complex midi phrases in real time.
This video will give you a more precise idea of what arpeggiators do. – PDG