Tag voting isn't supposed to exist, it was removed around 9 years ago now, but still exists in my mod, because I didn't want to remove a feature that might be useful. Since the Android port is based on my mod, it also has this.

My prevailing theory is that voting on tag influences the in-game search results. For example, if you search "city", you'll find a bunch of saves with city in the title and in the tags, but some of them are ranked higher than others, not only by votes. Perhaps someone voted the "city" tag on some of these saves.
For as developed as my theory is, I haven't ever found anything in the website code that would actually handle this. I don't have too much visibility into how the search works. There's an equally good chance that voting on tags does nothing.