The donut (yes, that is what it's called) is an Altmetric Badge and it helps track the spread of scholarly works through social media, the press, and other parts of the web.
"So, what does the number mean?"
The number is the "Altmetric Attention Score" and it provides a weighted score based on mentions from various sources. A newspaper article is an 8, while a Facebook post is 0.25. You can find more details about how the score is calculated and what the colors in the donut mean on Altmetric's site.
"Hey! My stuff's been talked about all over the place, why doesn't it have a badge?"
Right now only items which have a DOI listed can have an Altmetric Badge. We're working on ensuring that all items with a DOI have it in the right place so that it can be detected. Please get in touch with us at firstname.lastname@example.org if your work has a DOI that is not listed in Digital Scholarship@UNLV.
"My [article/thesis/poster/etc.] has a DOI and it still doesn't have a badge. What gives?"
Only items with an Altmetric score over zero will have badges appear. Not having a badge doesn't mean your work isn't being talked about, it just means that Altmetric isn't tracking where it's being mentioned. For more information about this you can take a look at this page about popular articles with low scores.
"Okay, that's all well and good, but what does it do?"
Mousing over the badge will cause a popup to appear and display a breakdown of the score. Clicking on the donut will bring users to the Altmetric details page for that item, where they can explore more in depth data, such as the original sources that mentioned the item.
"Does someone's work really have a score of over 4000?"
Yes! This article in Nature about a paper Stephen Hawking wrote about the (nonexistence) of black Holes has one of the highest scores and shows the many different places where Altmetric tracks mentions. As far as we know none of the items in Digital Scholarship@UNLV have scores that high (at least not yet!).