Article count badges
Turn on Show article counts on the Design page's Behaviour section, and each tag pill shows how many articles carry it: "Recipes (12)" rather than just "Recipes."
Where the number comes from
The count is the same one the nightly crawl uses for the "Most articles" ordering mode; it isn't computed live when a reader loads the page. If you've just published several new articles under a tag, the badge may be up to a day behind until the next crawl runs, or until you click Refresh tags.
Article vs. tag counts
The number next to a tag is how many articles carry that specific tag, not how many articles are in the blog overall, and articles carrying several visible tags are counted under each one. A 40-article blog where every article has two tags will show counts that, added together, come to roughly 80: that's expected, not a bug.
Note
This is a Plus feature. On the free plan, counts are hidden even if you've enabled them before and later downgraded. See Upgrading and downgrading for what a plan change does to settings like this one.