I have seen a lot in medieval reconstrunctions like this, that the side opposite to the spike is not flat, but have cross notches (sometimes very pronounced, like in the example). Does anyone know what is this? Of course it has to do because the weapon is used as a piercing armor, but, what is the specific role of these?
These weapons were usually wielded by infantry that fought "heavy" armor units. They would swing them at the opponent to inflict damage to the armor in hopes it would carry through to the person under it. Like Mark says the finer the point the more PSI you get.
However, typically there was a piercing side and a "blunt" side. The "blunt side" was used for disorientation and armor destruction. If you could deform the armor enough it wouldn't hold together very well. The pointed side was typically used to grab and puncture. If you scored a head shot with the blunt side of the weapon, bringing it back the other way was a good way to lance through a soft spot in the armor.
The reason they didn't always just go for the kill was your sharp part of the weapon was usually weaker and could get stuck in armor so you could actually snap it in battle if you weren't careful. Using blunt force was a better way to open the target up for an easier kill shot. The raised parts on the "blunt" end were just to maximize the PSI of the strike against the armor.
In your example, notice how the notches are shaped. They are pretty beefy, wide like sharks teeth and spaced widely apart. If this was actually used in battle it would drive all the force through those points, possibly puncturing the armor but would be easy to retrieve since they don't go very deep and are shaped not to get stuck. Hope that helps.
Flat against flat dissipates force and increases the chance that the hammer will glance off armor. (remember that armor is not flat - it is curved and angled to deflect blows and minimize the transmitted force).
Nubs concentrate force and reduce the chance that the hammer will merely slide off the armor. The blow is more likely to convey the force to the inhabitant of the armor.
And mea culpa - this answer would be improved by sources. @T.E.D found this discussion of engineering constraints in blunt weapons that is pertinent
In a comment to another post, I mentioned that years of martial arts training and acquaintances who like to hit each other in simulated historical combat have taught me that it is perfectly possible to break bones or kill an opponent without breaching armor. Even if the armor is intact, sufficient force can break the bone or cause a coup-counter-coup concussion. But that relies on maximizing the force delivered through the armor.
@EvanM's answer is excellent and superior to this one.