A cystidium is a big, funny-looking end cell that sticks out of a gill surface but doesn't look like a basidium. In this image, you see a gill surface formed of a palisade of end cells, the rounded basidia sticking out with their "crown"s of spores, and then the cystidia, even bigger than the basidia, bluntly pointed. Since cystidia have so many shapes, and these shapes hold (fairly) constant for a given species, they are useful in identifying mushrooms.
Distinctive cystidia have been used to identify mushrooms ever since they were first discovered. Here, the distinctive "crowned bottle" cystidia shown in the previous picture are depicted as a characteristic feature of the Plutaceae, in 1817.
Sometimes the cheilocystidia are strongly colored, and make the edge of the gill or mouth of the pore differently colored from the rest of the gill or tube, and their presence makes the gill edge seem fuzzy or finely fringed, even though they can't be clearly seen individually. The brightly colored pore surface of the red- and yellow-pored boletes is due to their cheilocystidia: the rest of the poretube is not colored the same way. In fact, some cystidia are specifically named after their golden appearance under the microscope: these are called chrysocystidia. You can see an example of dark-colored gills colored white at the edges by cystidia at http://www.cx.sakura.ne.jp/~kinoko/01eng/psathyrella_bipellis2.htm
So, you now have two possible ways to detect cheilocystidia without a microscope: they are sometimes differently colored than the face of the gill, and they are sometimes large enough to make the gillmargin look finely fringed (use a hand lens!). There is a third method: the cheilocystidia serve an excretory function, so the margin of gills with abundant cheilocystidia are often beaded with tiny droplets of liquid.
I lied before, when I said that cystidia look different from the basidia. Sometimes the cystidia can be roughly the same shape as the basidia, and then there is usually some controversy over whether to call them cystidia or basidioles or paraphyses, or whatever. However, even if the cystidia are roughly the same shape as the basidia, they are usually much bigger and that settles the matter of their identity.
Mycologists have acquired the habit of calling cystidia "sterile cells" on the hymenium. This is thoughtless, and I can only assume that they do it because they read it in a thoughtlessly written book as an undergraduate and then never thought about it again. Presumably, these books call cystidia "sterile" because they don't produce spores (as opposed to the basidia). If so, then all the other types of cells on the hymenium also need to be called sterile, and so does the entire mycelium of the fungus. Come on, people: not bearing spores is the default condition for hyphae, not a special one; as such, it needs no special mention.
