What is a Mockingjay?
A mockingjay is a bird that was created through inadvertent crossbreeding of jabberjays and female mockingbirds. When Katniss Everdeen wore a pin with this bird on it in the 74th Hunger Games, the Capitol was angry as it represented a slight against them due to the mistake that caused their existence. This is why Katniss became "The Mockingjay" and led the rebels in Mockingjay.
A hybrid of mockingbirds and jabberjays, the birds were created by mistake. The jabberjays - all male - were initially created to eavesdrop on the rebels in the Dark Days, memorizing entire conversations and repeating them back at the Capitol. Once they were discovered, the rebels fed endless lies to the birds, and sent them back loaded with false information. After the lies were discovered, the Capitol closed the laboratories and the jabberjays were released into the wild, in the hope that they would die off. They did, eventually, but not before they passed on their genetic code to female mockingbirds. This was unforeseen, because no one expected them to be able to reproduce with other bird species.