Probably has to do with control of the trunk and "infrasonic vocalizations"
http://www.karger.com/Article/PDF/345565
if you believe the cerebellum mainly contributes to movement. Some argue that it also contributes to "cognition", as Herculano-Houzel points out. Interesting that her group previously reported that, across evolution, brains maintain a linear relationship between number of neurons in neocortex and number of neurons in the cerebellum:
https://www.ncbi.nlm.nih.gov/pubmed/20300467/.
The finding that 97.5% of neurons in the elephant brain are in the cerebellum would seem to contradict the idea that brains maintain a constant neocortical/cerebellar neuron ratio. The elephant paper attributes the huge number of cerebellar neurons to sensorimotor input, i.e., probably trunk stuff:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4053853/