This allows you to fight notorious monsters against who you can wager gil (double or nothing), beasmens seals (75 exp each or nothing), or equipment (same eqwuipment with a random augment or nothing).
Basically, you do it for the augments. In particular, that chapter can be used with equipment levelled 10 or lower, fighting mobs in the areas directly outside the towns. Nothing too spectacular to be expected from them either - they may have elemental attacks randomly, but should go down pretty simply.
http://wiki.ffxiclopedia.org/wiki/Field_Parchment for more information.