Basically, reduced target effect, but with reduced ammo consumption. Suppression will give you a good reduction in Readiness on the targeted unit, but you will not likely get many casualties. But, it uses about 1/3 of the ammo a Neutralize mission does. If you knock the Readiness of a unit down to under 50%, then that unit is not likely to hit when it fores and really unlikely to get multiple hits.
Harassment uses hardly any ammo. So, what good is it? It might make an enemy decide to move off that hex. Don't expect casualties or a significant Readiness drop. A unit in Hold with decent Morale and Readiness will likely ignore it, though. It represents just a few rounds impacting.
I use Suppression when I need sustained fires on a target, like prep fires when making a deliberate attack. The defenders may be at full strength when I make the assault, but their Readiness is low enough that I get a lot more combat power making it to the objective.