I’ve previously answered a similar Quora question, “How does Cleverbot work?” , and have since blogged “My Cleverbot Tweet-FAQ” . Both Jabberwacky and Cleverbot were created by Rollo Carpenter . Jabberwacky  was created first (1997) by his Icogno.com and Cleverbot  later (2008) by Existor.com . Presumably Rollo is on Twitter at Existor . Notably, Rollo won the Loebner Prize in 2005 and 2006 with Jabberwacky / Icogno technology. Jabberwacky / Icogno technology is now behind both LifeNaut.com and LiveEnglish.ru .
Supposedly, Cleverbot is a variant of Jabberwacky, but more fuzzy and with deeper context. As for how Jabberwacky learns, Antonella De Angeli  and Sheryl Brahnam  published a 2008 academic paper, “I hate you! Disinhibition with virtual partners” , essentially an extensive analysis of the Jabberwacky knowledgebase. They state that “it learns by association, storing replies to inputs in a database”. For instance, Cleverbot uses 4d.com (4D v11 SQL).
I have posted a webpage, an informal survey of the past 10 years of academic work mentioning Jabberwacky . Jabberwacky is generally considered to use an AI technique called “contextual pattern matching”. I have not found evidence of any specific machine learning algorithms used in Jabberwacky; however, Jayen Ashar completed a 2010 PhD thesis entitled, “Online Learning in Conversational Agents” , essentially a literature review, which provides an overview of the field.