There are many definitions of famine.
There are also many theories to explain why famines happen. The three more welknown ones are the Malthusian (see Robert Malthus)view of agricultural production and population pressure on the land, Amartya Sen's economic causes and the complex emergencies theory.
'not enough food'
'enough food but market failure prevent distribution'
'enough food, markets failure exist, but fundamental causes of famine are political -man made'