Caveat - this is my interpretation of the various research pieces I've come across. I might be wrong.
It seems that having some period of starvation that is beneficial. Overall calorie intake is less relevant. Decreased overall caloric intake may actually be bad (can't find a link for this at the moment).
Benefits appear to include decreased risk of heart disease, type 2 diabetes and metabolic syndrome, possible decreased cancer risk, and decreased risk of neurological disease. Also longer life expectancy in some animals, as yet unproven in humans.
Even fasting for short periods regularly appears to be beneficial [5]
Three main reasons - autophagy, ketosis and decreased inflammation.
Autophagy, a kind of intracellular recycling operation, is increased by, inter alia, starvation [1]. It seems likely that most of the benefits of fasting derive from this. Valter Longo is a key researcher into this. Of particular interest to me is his work on fasting coupled with chemotherapy. [2]
Ketosis occurs when all your glucose and glycogen (a polymer of glucose) are used up, and you burn fat instead. Mark Mattson is a key researcher into this. Ketosis appears to have a neuroprotective action [3]
Decreased inflammation - chronic inflammation appears to be a cause of all sorts of problems, and fasting appears to decrease it.
[4] is a good general review
[1] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2831538/
[2] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3608686/
[3] http://www.sciencedirect.com/science/article/pii/S0165017308...
[4] http://www.sciencedirect.com/science/article/pii/S1550413113...
[5] http://www.medscape.com/viewarticle/861319
Use sci-hub for paywalled papers.