Paranodes are adjacent to the nodes of Ranvier. Here the spiraled lamellae of myelin gradually terminate.
http://www.bu.edu/agingbrain/chapter-3-normal-myelinated-ner...

See illustration here:
http://vanat.cvm.umn.edu/neurHistAtls/pages/images/Glia15.gi...

The term "paranode" is used in neuroscience to define a very specific type of cellular structure that, while not part of the neuron itself, plays an important role in excitatory signal transduction.

http://neuromuscular.wustl.edu/lab/schcell.html#ranvier
In the above link you find a couple of illustrations of a paranode.

The term paranode refers to the cytoplasmic region of the myelin internode that is adjacent to the node.
http://vanat.cvm.umn.edu/neurHistAtls/pages/glia15.html

Myelination organizes axons into distinct domains that allow nerve impulses to propagate in a saltatory manner. The edges of the myelin sheath are sealed at the paranodes by axon–glial junctions that have a crucial role in organizing the axonal cytoskeleton. Here we propose a model in which the myelinated axons depend on the axon–glial junctions to stabilize the cytoskeletal transition at the paranodes. Thus paranodal regions are likely to be particularly susceptible to damage induced by demyelinating diseases such as multiple sclerosis.
http://journals.cambridge.org/action/displayAbstract;jsessio...