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.
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)