[gone-ot]

wungun nailed the answers.

A wider gap increases the arc LENGTH (and thus AREA) within the A/F mixture between the electrodes, which provides better 'chance' of ignition of lean A/F mixtures which are often NOT easy to ignite--it's called increased "probability of ignition"--the difference in probability between a single-bullet and a shotgun-blast "hitting" the bullseye center of a target.

A narrower gap decreases the arc LENGTH in favor of a slightly HOTTER and LONGER arc duration, but assumes the A/F is always rich-enough to ignite easily.