Typically , accordian folds are simple zigzag folds with six panels and two parallel folds that go in opposite directions. Each panel of the accordian fold is exactly the same size, so no adjustments need to be made to a document layout to accommodate this fold, as you might need to do with other types of folds.
Also known as Z-folds, accordian folds are similar to the pleats on the musical instrument known as an accordion (note the different spelling).
Tri-fold brochures, business letters, invoices and monthly statements commonly use an accordian fold. This fold allows an address at the top of a typical portrait-style letter or invoice to show through a window envelope, avoiding the need for address labels.
Unlike folds where some panels have to be smaller to nest properly with each other, with an accordian fold, the panels are all the same size unless you are using one of the variations described below. This makes it much easier to set guides, margins and gutters during page layout.
Variations include half-accordian folds where one panel is half the size of the others, and engineering folds where one panel is twice the size of the others. Eight and 10-panel accordian folds are also common.
Note that a six-panel fold may be described as a three-panel while an eight-panel may be described as being a four-panel layout. Six and eight refer to one side of the sheet of paper while three and four are counting one panel as being both sides of the sheet. Sometimes "page" is used to mean a panel.
C Folds or letter folds are a common six-panel spiral fold for brochures and newsletters.
Spiral Folds with three parallel folds produce an eight-panel piece.
Double Parallel Folds produce eight-panels.
Gatefolds have six panels, with the middle panel double the size of the others.
Double Gatefolds have eight panels of approximately even size with two ends folded in.
See Folding a Brochure for measurements for three different sizes of a variety of ways to fold a brochure.