Bio Balls are black plastic balls specially designed so as to provide lots of surfaces within the area they occupy. Bio balls come in many sizes, colours and designs (there are even some that are not spherical but in the shape of cubes). The most common bio ball is the spherical, black bioball.
Bio Balls are used for biological filtration. The main advantage of bio balls over other biological media is that the surfaces are impossible to clog up (when used with a prefilter) compared to the micropores of porus ceremic material. The reason is simple: the gabs of space within a bioball is large and anything that can clog it up would already have been filtered by the prefilter (such as filter wool, sponge etc). This is the reason why water filteration should always pass through mechanical filteration (prefilter) before biological filteration.
On the other hand, other biological media such as ceremic rings owe their vast surface areas to their porous property. Porous means full of holes. And these holes are extremely small. In fact, these holes are so small that they can get clogged even by tiny water particles and sediments that cannot be filtered out by a prefilter due to their tiny size. Once these tiny holes get clogged up, there goes your super football fields of surface area.
Bioballs are sometimes misunderstood to be "nitrate factory" without using a prefilter. In reality, all biological media are nitrate factories without mechanical filteration (prefilter). Nitrates is the end product of the nitrogen cycle. Without a prefilter, solid wastes and uneaten food scraps end up sitting on the biological media and ultimately breaking down into nitrates. A prefilter would have allowed these these foods and solid wastes to be removed before they have the chance to break down into ammonia, to nitrites and then to nitrates. If you have followed the logic, you would also realise that if you do not maintain your mechanical filteration regulary by replacing or washing, then it will be a nitrate factory as well.
The main advantage of bioballs over other bio media is not only its uncloggability, it is also the aeration it provides. Their large gabs allow air/oxygen rich water to enter to mix with the dispersed water surfaces, so there is excellent interaction between air and water and gas exchange. And don't forget that oxygen is essential for the conversion of ammonia into nitrities and then to nitrates by aerobic bacteria. For this reason, bioballs are best when used in a wet-dry deployment. Wet-dry sounds confusing, but the concept is simple. If you stand up in the shower and have the showerhead spray water on you, you are in wet-dry. Yes you are wet, but not fully wet, parts of you is dry. When the water flows down your chest, your back is dry. When the water flows down your back, your chest is dry. If you immerse your whole body into the bathtub, your body is not wet-dry, only your head is. If you got that idea, then picture water flowing down through bioballs that are sitting above the water level in a sump. That is wet-dry. Bioballs in a canister filter is not wet-dry because it is always wet.
Bioballs is an excellent bio media, its only drawback is it takes up space. If you have the space, use bioballs for all the reasons mentioned above.