Unlike most other spec differences, monophonic vs. polyphonic isn't a matter of taste - it directly determines whether you can play chords at all.
Monophonic
A monophonic (mono) synth can only sound one note at a time; playing a new note while holding another cuts off (or in some designs, glides to) the previous one. Many classic bass and lead synths are mono by design, since a single, focused voice suits those roles and mono synths are historically often simpler and cheaper to build.
Polyphonic
A polyphonic (poly) synth can sound multiple notes simultaneously, up to its voice/polyphony limit (see our separate article on polyphony and voice stealing), which is required for chords, pads and most conventional keyboard playing.
Paraphonic - a middle ground
Some synths are "paraphonic": multiple notes can sound together, but they share a single filter and envelope rather than each note having a fully independent voice - a distinct third category worth knowing about since it isn't quite either of the other two.
Before buying a used synth for a specific role, checking whether it's mono, poly or paraphonic matters more than almost any other spec - a great-sounding mono bass synth simply cannot substitute for a chord-playing pad synth, regardless of price or reputation.
