This is part of the binding process for hardback books. Basically it refers to putting the case onto the book block. The signatures making up the book have been through the gatherer, and are now assembled in sequence. The first and last signatures will have had the endpapers tipped to them before the were put into the gathering machine. The assembled sigs look like this.

Photo: Bible Design Blog
The marks running down the fold provide a visual warning in case any sigs are gathered out of sequence. With longer books it is not uncommon to see two slanting rows of marks.
Forwarding begins now. The first step is to join all the sigs together into a book block. This almost always used to be done by sewing. (It’s Smyth sewing, not Smythe.) The signatures are placed in sequence over a sort of saddle and a set of needles pushes thread through the fold at the spine edge, joining each signature to the preceding one, until the entire book is sewn together in one block. (You can see this process in the video below.) Sewing is being used less and less, because it costs money, and we now tend to use glue to hold the signatures together.
The spine will be glued and linings (two different types usually; crash and mull) are applied as are the headbands. The sides of the book block (the outside of the endpapers which are tipped to the sewn sigs) is glued and the case is placed over the book block.
Building in forms the joints, compresses the book, secures it firmly in its case. This is all done nowadays in-line, but used to be a separate step in the binding process. In this video you can see the book being rounded and backed by a roller press and an operator with a hammer. This is rather rare today. In the old days the bound books would be stacked with spacer boards and compressed overnight to ensure the joint and the round were well formed and permanent.
(Link via Shelf Awareness)
[…] The case for a hardback book consists of four pieces of material. Three pieces of cardboard, binder’s board, are cut, two the same size for the front and back cover, and one the same height but only as wide as the spine of the book. The spine board will, unless we are dealing with a square-back book, be much thinner than the front and back boards. The spine on a square-back doesn’t have to bend, so can be the same thickness of board as the side panels. A bit of book cloth, cut to size, is glued up and the bits of board dropped into position. Nowadays, rather than a woven fabric which will be stronger and longer-lasting, we often use a paper product for covering material. It’s cheaper. The edges of the cloth are turned over and stuck over the edges of the board. The cases are transferred to the stamping department where the title etc. will be foil-stamped onto the spine, using pressure and heat. And lo and behold we are ready to stick the end-papered book block into the case in the process called forwarding and building-in. […]
[…] mechanism of the hinge originates as a part of the rounding and backing process, where the edges of the book block are splayed outward under roller pressure to create lips […]
[…] end up being squashed into even dispersal. But if it’s near the edge the pressure applied in building in will make it squirt out and dribble down the book’s trimmed edge. Because it starts life […]
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[…] A horse of a different color is the book block. […]