Feedback loops enable ISPs to forward email complaints from their users to the email's sender. They provide valuable feedback to both ISPs and marketers on what users consider to be "spammy".
Many ISPs implement a "this is spam" link, or an equivalent link or button in their systems. When one of these links is used by the ISP's subscribers to flag an email as spam, a number of things occur.
Many email users, after hearing that spammers use unsubscribe links to verify that an address is active, rather than actually unsubscribing the recipient, have made a habbit of flagging emails as spam, rather than clicking on unsubscribe links. This is further reinforced by ISPs (arguably correctly) blocking all future emails from that particular sender to the complaining subscriber. As a result, even the cleanest of email lists which send email that most would not consider to be spam will sometimes be reported as spamming.
Feedback loops are a valuable source of information to ISPs and email marketers. They provide one of the most accurate metrics available on how "spammy" an email campaign is perceived by its recipients as being, and help ISPs to more accurately filter spam, while allowing legitimate emails through.
The three most significant email service providers which offer feedback loops are:
Gmail is noticeably absent from this list. Google does not currently offer a feedback loop to senders.