I believe that the counter is showing a "3" because several posts that were flagged as "low quality" appear to remain unresolved.
First of all: as C. M. Weimer says, the counter is showing the total number of pending reviews in the system. When the feature was rolled out, there was a lot of consternation about this, because many people wanted an individual counter, not an overall counter. But that would be too resource intensive, so the SE developers didn't implement it that way. See: Notification for reviews shows way too many.
Theoretically, then, the "3" could appear for several reasons:
- You (as an individual) have something you could review in one of the six review queues
- You clicked "skip" on something in one of the review queues, causing it to disappear from your own queue but remain present in the system
- You took an action, but other people have to take action as well before it disappears
Several of us agree that we have nothing in any of the six review queues, so (1) doesn't apply. Personally, I know that I haven't skipped anything, so (2) at least doesn't apply to me.
That leaves (3). Several actions require multiple reviews before they are "resolved," and they are:
- Close votes
- Reopen votes
- Suggested edits
- Low quality posts
The 10k tools page reveals that there are zero questions that have outstanding close or reopen votes, so that's not it. That leaves suggested edits and low quality posts. For a suggested edit to be resolved, it needs either two votes for approval, two votes for rejection, or one vote either way by the OP. Right now, according to the history, every suggested edit has been resolved one way or another.
So that leaves us with low-quality posts. The process for low-quality posts is that first they pass through the Low Quality Posts queue, where users with 1k or more reputation can "recommend deletion." But in order for these posts to be "resolved," one of five things has to happen:
- Six users (>1k rep) recommend deletion (source)
- Three users (>4k rep) vote to delete (we don't have anyone with this privilege at the moment)
- One moderator deletes
- A substantial edit
- Several users say "Looks OK" (see When is a post removed from a review queue?)
The history of our Low Quality Posts review queue reveals that there are probably three answers that have not fulfilled any of these criteria:
- The first has two "Recommend Deletion" and one "Looks OK"
- The second has three "Recommend Deletion".
- The third has two "Recommend Deletion" and two "Looks OK"
I believe that it's these three answers that are still "pending" and causing the counter to show "3."
So what do we do?
It's unlikely that we'll get Stack Exchange to change the behavior of this counter. So what can we do to get the counter to zero?
- Probably the least viable option would be to wait until we have three users with 4k rep. They would be able to delete the offending posts if they all agreed.
- Alternatively, we could encourage all 1k-users to go to the low-quality posts queue and review. But even if they do, reaching six recommend deletion votes is tough to do for a small site like this.
- The simplest approach would be for a moderator to delete or preserve the three answers. It may still be several weeks before we get our own moderators, so asking a community manager (like Robert) to address these would be our only short-term option to clear these out.
However, let's also consider that on many sites, particularly medium and large ones, the counter at the top of the screen is a fact of life for all 10k users: it simply doesn't go away.
It's theoretically possible for each site's moderators to unilaterally clear all the review queues to keep the counter from appearing. But that's not how Stack Exchange is designed to work: the community is to be involved in moderation, not just moderators, and that means that moderation can take time.
In the long run, we'll keep the counter down by working together to flag and review questionable posts, with moderators taking action in egregious cases or once the community has expressed itself through reviews.