Thus, this priority represents the current depth (or height) of the DAG at each node. It is sort of a timestamp and you could use a timestamp, or whatever helps you sort. In the case of concurrent writes, the write with highest priority wins. If we have concurrent writes of same priority, then things are sorted by CID.
The idea here is that in general, a node that is lagging behind or not syncing would have a dag with less depth, therefore its writes would have less priority when they conflict with writes from others that have built deeper DAGs. But this is after all an implementation choice, and the fact that a DAG is deeper does not mean that the last write on a key happened "later".