Rhizomatic learning is a theory of learning best known from its use in connectivist MOOCs like #rhizo14 
and #rhizo15 It can be compared to connectivism.
A rhizome is a botanical concept: "a rhizome is a modified subterranean stem of a plant that is usually found underground, often sending out roots and shoots from its nodes." wikipedia
Deleuze and Guattari (D&G) use the metaphor of the rhizome to talk about a type of thinking that is non-linear. They compare rhizomatic with arborescent thinking. Cath Ellis illustrates this on her blog here Most of their writings on the rhizome are in A Thousand Plateaus
Dave Cormier has done most of the work around rhizomatic learning, which is an extension of D&G's metaphor. Cormier suggests that rhizomatic learning is a means by which learners develop problem-solving skills for complex domains. html Elsewhere he has talked about it as a story (not a theory) about how meaningful learning can occur in an age of abundance.html
It's important to remember that the rhizome is not a model for this type of learning. At best it is a metaphor (as Hamon writes here In particular: "The rhizome of Deleuze and Guattari is not a homogeneous botanical system; rather, heterogeneity is one of the six characteristics of their rhizome.")
We're attempting to get this written up as a wikipedia article. more here