RIMS stands for Recirculating Infusion Mash System. If you are familiar with the all-grain brewing process, then you know that mashing is the process of mixing your milled grain in with hot water and letting the mixture rest for a period of time. Enzymes found naturally occurring in the grain are activated by the heat and water so that they begin to break down the starches within the grain into sugars that the yeast can ferment into beer. While there are different ways to get the mixture of water and grain to the proper temperature, this particular method of mashing (heat water, mix with grains, let rest) is called infusion mashing. Because of its simplicity it is the preferred method of many homebrewers. Therefore, many all-grain homebrewers are just one step away from a RIMS. By adding a pump to your mashing vessel (mash tun) and recirculating the wort as you mash, you will have created a simple RIMS and will be able to obtain some of the benefits of such a system.
While the above described system could reasonably be defended as a RIMS, most RIMS users will also include a source of heat in their definition. The purpose of additional heat is to more accurately control mashing temperatures. There are different ways to provide additional heat to your RIMS, such as firing your propane burner beneath your mash tun (assuming it's metal) or firing a smaller flame-burner on a metal coil that the wort is recirculating through. However, the most common method of providing additional heat to your system is by placing an electric heating element, such as from a hot water heater, in the plumbing of your recirculation so that the wort can flow across it and be heated.
And finally, there are some RIMS purists who define a RIMS strictly according to the original RIMS designed by Rodney Morris. Rodney was able to automatically control the temperature of his recirculating wort with the addition of some home-built electronics to his heating element. By placing electronic temperature probes in his plumbing, and then connecting these probes to his electronics and his heating element, his system is able to measure the temperature of his recirculating wort and adjust the power to the element accordingly. Rodney is therefore able to dial in a target temperature and the system will at first provide maximum power to the element, but as the temperature of the mash begins to approach the target temperature the power to the heating element is reduced so as to prevent the system from overshooting the target temperature. The system will then maintain this set temperature without any need for manual intervention.
Iam not as electronically inclined as Rodney. Therefore my first attempt at a RIMS system did not use the same level of automation that his does. I used bimetal dial thermometers instead of electronic temperature probes, and my eyes, brains, and hands took the place of his electronics. While the purists may have described my system as a "pseudo" RIMS, I think most people agree that as long as you recirculate your mash, and maybe provide additional heat, then you have a full-fledged RIMS.
Eventually I was able to upgrade my system to be more automated so now it is definitely a full-fledged RIMS. Still, I'm no electrical engineer, so I solved this by buying a gadget called a PID temperature controller. More detailed information can be found within these pages, but basically a PID temperature controller does the same thing as Rodney Morris's temperature controller only better. It is a miniature computer the size of a small radar detector that takes a temperature reading of the wort via a thermocouple and adjusts the power to the heating element accordingly. Its sophisticated "brain" actually "learns" how your system reacts and uses calculus to determine how to boost your temperatures to your desired set point as fast as possible and then backs the power off as it gets close so as not to over shoot the set point temperature. So now I simply enter the set point temperature on the digital read out and it does the rest!