Mockingjays are a mainstay in The Hunger Games series. They are a fictional creature, existing both as a symbol of resistance and an actual bird.
The Bird
They are said to be products of interbreeding between mockingbirds and jabberjays, the latter of which is a fictional "muttation" created by the Capitol during the First Rebellion. Their fathers, the all-male Jabberjays, were genetically modified to be able to store and recall up to a full hour of conversation, and be controlled by a simple remote. They were used for spying and intelligence gathering, obviously. Eventually the rebels figured this out, and began to feed the jabberjays false information, leading to a discontinuation of their use. Widely regarded as a failure by both the Districts and the Capitol, they were released into the wild, where it was thought that they would die out. Indeed, while the jabberjays did die out, they managed to mate with the native mockingbird population, producing mockingjays.
While mockingjays can't recite words themselves, they can easily memorize snatches of melodies, and repeat them. This is actually used in the first book to pass along a message via a whistled tune. They seem to also be very social birds, as large groups of them can be heard passing along and morphing songs when out in the forests.
The Symbol
The Mockingjay is used as a symbol of resistance for the oppressed districts, mainly due to its association with their hero Katniss Everdeen and its being a representation of one of the many failures of the Capitol during the First Rebellion. Its association with Katniss is due to her wearing it as a pin in the first book during her stint in the arena. It was seen by many and featured prominently across the televisions of Panem, and eventually stopped just being her symbol and became the rebellion's symbol.
Despite my views on the books as being only mildly enjoyable (a bit too focused on love triangles for my taste), the Mockingjay is up there on the list of my favourite fictional creatures. When it comes to the category of small birds, I should say. It has a very succinct yet interesting explanation for its existence, and they're also given a significant symbolic purpose in the story. They are easily one of Suzanne Collins' most carefully crafted ideas in the books.