One bank sends a check to another one. The first bank needs to know if the check is good, whether there's money in the account, and whether the second bank will issue payment or not.
In the old days, this actually meant that the first bank physically sent a piece of paper to the other bank. It was a process that could take some time, if the two banks were far apart from each other, like in another state.
However, waiting for a reply could cause problems. The first bank doesn't know how much money they will have. Is that check good or not? To alleviate the suspense, the second bank would send a quick reply via telegraph.
That reply was known as a Wire Fate Item. It was an item, sent by wire, that informed the original bank of the fate of the check.
Nowadays, the term applies to the general process of confirming the payment of checks, though the modern system, using online communication, has moved well past the telegraph part. For that reason, the phrase "wire fate item" (and the concept it represents) is considered old-fashioned.