A "manufactured" bid is one which does not meet the usual requirements for the bid made. It is used when the player must bid something, but there are no other good bids, but it isn't just a random bid. It must be made with a plan on what to bid next depending on how partner responds.
ACBL Bridge Bulletin March 2022, p.38 #2, Bid Box says: "The strategy of 'inventing' a jump-shift in a minor... can be an adequate solution to many of opener's rebid problems." Here, the hand was considered too strong for 3
, especially considering the secondary spade fit: 
AQ2 
AKT765 
A 
JT5 with bidding of 1-P-1
-P - 3
.
From July 2018 ACBL Bulletin, p.53:
Eddie Kantar shows this hand: K4 AQJ7 94 AKJ54 with bidding of 1-1, ??.
Answer: A made-up ("fake") reverse of 2
which is forcing and shows your strength. Next you will raise hearts which, with your bids of clubs and diamonds, indicates spade shortness.
From the August 2023 ACBL Bulletin, p.37:
East: 9 AKJ7 932 AKQJT
Bidding:
Opener (East) wants to make a forcing bid but what? The bid chosen was 3.
Now West must figure out what 3 means:
If East has a balanced hand, he most likely would have bid 3N.
If he is 5-5 or even 5-6+ in and , he would have opened 1.
East's failure to support either Spades or Diamonds tends to deny 4 of either.
Finally, East started with a reverse, showing a big hand.
The above tends to draw a pretty full picture of his actual hand.
West can now merge that information with his own hand and bid accordingly.
West's hand: AKT76 Q4 AK75 86
With his 16 HCP, West can be pretty confident that his side has a slam but also a misfit, so he manufactures a 5N, which supposdly means "Pick A Slam", but West's intention is to convert any response to notrump.
East bids 6, with his extra honors making up for the lack of a 6th Club and West comes back with 6N.
Now it's time for East to ask himself why West didn't just bid 6N to start with. The actual East spoiled the story by simply passing 6N, but the moderator said that if West reasons that the most likely reason is to invite a grand slam, then East can bid on.
In this case, he would have East bid 7 and then West would correct to 7N.