Perforations are the holes punched between individual stamps to allow them to be easily separated from a sheet. Not all stamps are perforated, especialy early issues that were cut from the sheet with scissors - these are known as imperforate. Some modern stamps may have an imperforate variety that was usually targeted at the collector market. Where a stamp is perforated around the border it is catalogued according to the number of holes over a set distance called its "guage". Where a single number is given in a catalogue it means the stamp has the same guage on all edges. Where 2 numbers are given, the first is the horizontal guage and the second is the vertical.
At left is the simplest tool for determining guage of a stamp, To use it, a stamp is simply placed on it and moved up or down until all the peaks of the perforation fall on a vertical line with the corresponding guage taken from the numbered scale along its left edge.
Our club has an electonic guage for use at meetings and there are also "apps" available for smart phones that will determine a stamps guage using the phones camera.
An alternative to perforation was "rouletting" which involved putting tiny slits in the paper between the stamps allowing them to be separated, The same guage is used for measuring rouletted stamps.
Australia used a special perforation for some of its early issues intended for use as coils in vending machines. These stamps had larger holes at the central portion of the stamp than the outer edges. The sides of the stamps were uniformly perforated.
These "coil perforations" are usually collected in pairs or strips as once the individual stamps are separated it is impossible to distingush them from normal sheet stamps.
Other stamps can be found with a series of holes forming letters punched in them. These are called "perfins" and were a way of stopping theft of unused stamps from government departments or private companies. The letters OS were punched into Government departmental stamps in Australia. The individual states would also sometimes use perfins so it is not uncommon for stamps to exist with SA, NSW, WA etc punched in - especially on colonial era stamps. Again there is specialist reference material covering these and it is an example of the diversity that can be persued in philetalics.