Ceremic rings are also known as bio rings for the reason that it is used for biological filteration. Ceremic rings do not look like your wedding rings. In fact, they are in the shape of mini toilet rolls.
Ceremic rings wildly touted as new technology, scientifically crafted etc etc. In fact, they are just porous materials with a lot of tine holes, tunnels and yet more microscopic holes and tunnels. These pores are what gives it it's large surface area. Surface area is of utmost importance in biological media because that is where beneficial bacteria grows on. The more surface area there is, the more space there is for beneficial bacterial to colonise. These bacteria converts toxic waste ammonia into less toxic nitrites and then to relatively harmless nitrate.
Due to their porous nature, their tiny holes(pores) can get clogged by tiny waste particles that cannot be filtered out by a prefilter. When they get clogged, all their football fields of surace area will disappear. The bacteria at the end of the blocked micros tunnels then could not access they waste they are supposed to process. For this reason, ceremic rings should be washed regularly, how often depends on how fast they get clogged, the texture of the food you feed to your fish etc. The most important and crucial thing to note is that when you wash the media, do not wash them under tap water. Instead, wash them with water you siphoned out from your main tank. It is also important that the water you use to top up the water volume in your tank be properly treated with antichlorine/antichloramine, especially in this particular maintainance session where your bio media is washed. You are advised not to change or wash your prefilter (ie filter wool, filtersponge) when you wash the porous biological media because a LOT of tiny particles will be loosened out from the pores they were stuck in previously. A dirty seasoned prefilter is better able to trap these tiny particles. After a day, some of these tiny particles would have been trapped by the prefilter, the rest would have gone back to the pores where they came from. However, your bio media washing have not been in vain, because a big portion of the micro particles have been washed away. This gives a refreshing new life to the beneficial bacteria in your bio media, because they are suddenly given more space to "breath". (Much like caged chickens released into wheat fields)
As you have probably known by now, the main advantage of ceremic rings/bio rings/porus media is their large surface area. If you have a space restriction and have to cram as much surface area as possible into a small space, then ceremic rings is the biological media of choice.