A rhetorical figure meaning to reject an idea emphatically. Literally, to chase away. The word is from the Greek "apo" meaning "away" and "diokein" for "pursue".
An apodioxic rejection implies that the speaker cannot even understand the premise of the claim being rejected- it is absurd, needless, dangerous, evil, or simply utterly and obvously false.
Frank Booth's beer preference in David Lynch's film Blue Velvet serves as a nice example of apodioxis:
Heineken? Fuck that shit! Pabst Blue Ribbon!
Apodioxis expresses rejection of and dislike of an idea (such as the idea of having a Heineken, which Jeffrey Beaumont brought up), while bdelygmia expresses hatred or dislike of a person or thing. The difference is subtle: A thing versus the idea of a thing. Luckily, it doesn't matter one whit.