A Flypress is a metalworking machine tool used to punch holes in sheet metal in one operation, rather than by cutting the hole or drilling, etc. The machine is manually operated - powered presses are also used but are not usually called flypresses.
The manual machine works by using a coarse screw to convert the gross rotation of an overhead handle into a small downward thrust with the force multiplied up considerably. The overhead handle is usually counterbalanced using a flyweight (hence the name of the machine) - this weight helps to maintain the momentum and thrust of the tool as it punches through the material.
The tool itself consists of a punch and a matching die, into which it very closely fits. Both are usually precision machined and then hardened. The material is introduced between the punch and die, and the machine operated. The punch will cut through the material in one movement by shearing it.
The punch and die may be of any desired shape, so odd shaped holes and cutouts may be performed. Precision laser cutting and other techniques are more often found in modern production facilities.