A wort chiller is a device used to rapidly cool the wort after the boil has completed. Typically the wort is knocked down from boiling temperatures to less than 80° F as quickly as possible so that yeast can be pitched. Once the wort falls below boiling temperatures, it becomes susceptible to bacterial and wild yeast contamination. It is important to get the wort below 80° F without splashing or aerating it too much, as hot side aeration can oxidize your wort above that temperature.
There are three typical types of home brewing wort chillers. Immersion chillers are large coils constructed of copper or stainless steel. They are placed inside the brew kettle while cold water is pumped through the chiller, cooling the wort. Plate chillers are made of fused plates and have channels where the cold water is pumped in from one end, causing it to intersect with the plates being heated by the wort from the other end, which rapidly cools the wort. Lastly, counter flow convolution chillers have hot wort flowing through one tube as chilled water passes over it from the opposite direction in a surrounding tube. I personally prefer the counter flow convolution chillers because they permit me to cool my wort quickly while also being easy to clean, since hops and trub are less likely to get lodged in the tube than they are in a plate chiller.
Below is a photo of three examples of home brewing wort chillers: an immersion chiller, plate chiller and a counter flow convoluted chiller.