"Flashing" is a general terms for updated the system partitions. It can mean inserting an individual app (via a custom version of the system recovery module) or overwriting the partitions completely with new system images. In the context of unrooting it means the latter.
Unrooting means undoing changes that the user made in order to "root" the phone, i.e. gain administrator access. Generally the simplest way to do this is to "flash" a set of stock software, i.e. completely replace the modified software with a copy of the vendor's original software.