What does the number in the column named renames in the list of tag synonyms mean?
Is it the number of questions that were tagged with the "child tag" when the synonym was created?
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It represents the number of times that someone has entered that tag and it was retagged to the master tag since the synonym was created.
So for example, given the relationship tag-synonyms ← tag-synonym, if I explicitly type out "tag-synonym" and hit space to format it as a tag, that tag will be remapped to the master tag. That will increase the count for renames, and update the "last"column as being the last time a rename occurred for that relationship.
It's basically a way of tracking how often users are typing out that specific synonym and having it remapped to whatever master tag it points to. A lot of synonyms, like tag-synonym, don't get many renames recorded because most users will select the master tag when it pops up in the tag suggestions and the actual tag rename never occurs.