Arpeggio
An arpeggio is the simplest type of broken chord: you simply play each of the chord's pitches, one at a time, in either ascending or descending order.
Ascending arpeggio
Some synthesisers can automate this with an arpeggiator, which is essentially a very basic form of digital step sequencer. It can usually be set to cycle the pitches in one of several patterns, such as ascending, or descending, or alternating between the two, or randomised. The musician only needs to hold down the notes of the chord, while the synthesiser takes care of cycling between them.
As an arpeggiator has to scan the keyboard for multiple simultaneous keypresses, then translate those into alternating pitch values, it needs to use a microprocessor. This is why arpeggiators are most often found on the polyphonic synthesisers that need them the least, as they already have a microprocessor to scan the keyboard and assign each note to a separate voice.
Electronically performed arpeggios can cycle between pitches much faster than a human hand can play notes, allowing a very distinctive sound that was one of the hallmarks of the Commodore 64's chiptunes back in the 1980s, as employed by musicians such as Matthew Cannon and Sean Connolly & Marc Francois.
There's something to be said for manually drawing in arpeggios on a sequencer, as you can come up with more varied patterns than simple ascent and descent, along with adding accents and rests. Then you've basically turned a simple arpeggio into a more complex type of broken chord, or even a fully fledged rhythm part.
Significantly embellished ascending arpeggio
Music theory: Arpeggio | Block chord | Broken chord | Circle of fifths | Interval | Music | Pitched tempos | Polymetre and polyrhythm | Rest | Swing | Velocity