A Connects refund is Upwork returning the Connects spent on a proposal when the job post is removed by Upwork, cancelled, or closed in other circumstances Upwork specifies, rather than when the client simply hires someone else.
Connects are spent at the moment a proposal is submitted, and in most outcomes they stay spent. Upwork's Help Center lists the cases in which they come back: a job post that Upwork takes down for breaking its Terms of Service, a client account that is suspended, a post the client cancels in circumstances Upwork sets out, and some others that Upwork has added or removed over the years. The list is set by Upwork, has changed more than once, and the Help Center is the only reliable statement of it at any time. Refunded Connects return to the account, or to the agency's shared pool when the proposal was sent by an agency, and Upwork notifies the sender.
What does not trigger a refund is the ordinary disappointment: the client reads the proposal and hires someone else, or never hires and lets the post expire. Withdrawing a proposal does not by itself return the Connects either. For Boosted Proposals the boost bid follows its own rules, and a bid that did not win a slot is generally not charged in the first place.
Because refunds are the exception, the way to protect Connects is before bidding rather than after: reading the client panel, the hire rate and the proposal count, and skipping posts that look unlikely to end in a hire.
How Upwork Insights uses it
This term describes Upwork's own rules or product rather than a figure the index measures; the pages that do carry live figures are the stats and rate pages.