Rhizomatic learning is a way of thinking about learning. A rhizome, sometimes called a creeping rootstalk, is a stem of a plant that sends out roots and shoots as it spreads. One idea is that, like learning, a rhizome has no beginning or end.
I heard about it years ago probably on Dave Cormier's blog. It has been associated with critical pedagogy, but it came into the zeitgeist again when MOOCs were surging around 2012 along with other emergent online learning practices.
It goes back further to a rather unlikely book, A Thousand Plateaus: Capitalism and Schizophrenia (French title: Mille plateaux). This is a 1980 philosophy book by the French philosopher Gilles Deleuze and the French psychoanalyst Félix Guattari. It talks about the work Sigmund Freud, Carl Jung, and Wilhelm Reich and does not seem like a book for educators. From what I have read about the book, it is a difficult read, or at least possibly a confusing read, because it is itself like a rhizome. The book is non-linear and the reader is invited to move among plateaux in any order. It has been both influential and criticized.
It spawned the idea of rhizomatic learning as pedagogical practices. This is something very much in the realm of learning theory and initially it was considered an application of post-structural thought to education.
It has also been used in discussions of methodologies for net-enabled education. As I said, the rise of the MOOC gave it a shot of interest again. In rhizomatic learning, the path is not goal-directed in the way of hierarchical theories of learning. If you follow this rhizomatic path, you would believe that learning is most effective when learners are allowed to react to evolving circumstances. In that way, this path is fluid and evolving based on the current task and how the participants deal with it. Therefore, it reminds some people of the way roots and rhizomes grow, avoiding obstacles, branching and connecting to other rhizomes while constantly seek nutrients and water as objectives for growth.
Though most online learning in formal courses does not follow this methodology, MOOCs and some less formal online learning where "the community is the curriculum" do not follow the traditional "instructional design" models. Most of us are used to setting objectives before students are involved in learning, but rhizomatic learning would allow most objectives to emerge, or at least allow for the order of objectives and the ability to add new objectives along the way.
I fall more on the side of George Siemens (who was one of "inventors" of the MOOC) who questions the usefulness of the rhizomatic metaphor. He prefers traditional network analysis, and though rhizomes are a way to describe the structure and form of learning, it doesn't provide a true methodology.