I believe the theory is that we are currently on an unsustainable path that is drawing down our existing inventories of global food faster than we are replenishing them (ex. overfishing of oceans), so to feed 1) our first-world selves, 2) our third-world friends who are becoming first-word (i.e. eating more food), and 3) an additional 2/7 population... that will require a growth in the food supply. I think some of those on the more doom-mongering side tend to underestimate the general agricultural innovations of both past and future, and the market forces that drive them, but there are some compelling arguments that this may not be enough.
A lot of today's population is underfed or suffers from nutrient deficiencies. To "feed" today's population we already need to increase the global food supply.
Here's a UN press release from 2009 titled "Food Production Must Double by 2050 to Meet Demand From World's Growing Population":