We are not talking about the signature where you sign your name or something green on a tree or something you walk around. Rather we are referring to three terms common in book printing.
A signature is a unit of pages that are formed when a press sheet is folded down to the finished page size. Signatures are always multiples of four pages. The most common press sheet size is 23" x 35" which is why you see so many books and booklets that are 8.5" x 11". You get eight 8.5 x 11 sheets out of a 23" x 35" sheet. If your printer has a large enough press he can print sixteen page signatures-eight 8.5" x 11" s printed on two sides. This is the most e economical signature size of all. Other common signature sizes are 12 ,8 and 4 pages. Each smaller size signature costs more per page. If you are printing on a digital press you are limited to 8.5" x 11" four page signatures because digital presses are smaller than real printing presses.
A leaf is a single sheet of paper with a page on each side. A book will have one leaf for every two pages. These are the building blocks of signatures. A book can have many leaves and will have half as many pages which will form in units of four to build signatures, get it?
A block or book block is what you have when you combine several signatures by sewing or glueing them together prior to applying the soft or hardback cover.
Now maybe you know a little more about how to build a book. When you are planning to print a booklet or book rely on you printer to explain the most economical way to print because they will understand the math, physics and geometry involved. It's not rocket science but it is more complicated that you might think-again, rely on your printer.