The records that were burnt were, typically, manorial rolls. These were records which detailed who had paid what to the lord of the manor and therefore were quite important for local administration. A modern parallel would be rioters storming the local town hall and burning the tax records.

They could be used to trace lineage but only if we had another source to ensure that the named individuals paying their dues could be linked to descendents or antecedents. They would have been more relevant at the time, of course, as they could prove lineage (and inheritance of dues) through other means - especially memory.