"Recurrent" might be the term you are looking for, i.e.:
running or turning back in a direction opposite to a former course —used of various nerves and branches of vessels in the arms and legs
If you observe a recurrent network within a single pair of neurons, you could also refer to this as a reciprocal connection, in that a pair of neurons are both post-synaptic and pre-synaptic to each other.
More generally, you could also talk about feedback as a general motif in neuronal circuits.
The function of recurrent connections likely depends on the specific network you are talking about, but they can be used for predictive coding, pattern generation, computation, and more. In organisms with 'simple' nervous systems like C. elegans, however, these connection patterns can be even more complex, because they have evolved to perform a lot of behavior with very few neurons.
Try searching Google scholar for recurrent neuronal circuits for some more information.