Rubber is one of the most basic components of almost every Template:IC2 machine. It is primarily used for insulating Electric Cables, which is a very important step in making electric machinery! Additionally, it is important to insulate any Cables you use to transport EU from one Machine to another, or you may be electrocuted from uninsulated cable. Even when players upgrade to Glass Fibre Cable (which do not require rubber), rubber is used to make Electronic Circuits.
Rubber can be obtained in several ways. The primary method is by refining Sticky Resin using a Furnace or Extractor. By smelting Sticky Resin in a Furnace, you get one piece of Rubber, but by Extracting it, you get three pieces. You can also obtain one piece of Rubber from processing either Rubber Wood or Rubber Tree Saplings in an Extractor. This method also works for Redpower 2 rubber trees, though note that you cannot extract rubber from the corresponding saplings.
Another way to get sticky resin is using the Redpower or IC2 rubberwood in a Thermal Expansion Sawmill, which grants you four jungleplanks and a 33% chance to get sticky resin. You earn much more resources by using this method.