Parry class defines whether an attack can be parried or not. All weapons (including fists) have a parry class ranging from 0 to 2. Any weapon can parry attacks from a weapon of equal or lesser parry class.
For example, if you're using a Lotus Nodachi (parry class 2) against a chobo wielding a pipe (parry class 1), you will be able to parry his attacks but he won't be able to parry yours. However, if we reverse the battle and you switch to your fists (parry class 0) he will be able to parry your attacks but you won't be able to parry his.
Parry class can be viewed by checking your "gear". The number of asterisks signifies it's parry class.