government

You are correct that there is plenty of food in the world today, and the problem is getting it to people who need it.

There are a number of issues involved, such as the lack of good roads in many parts of the world. Africa, for instance, has very few decent roads, so that transportation of goods overland in Africa can actually be more expensive than in a first world country.

However, by far the largest problem is government. There has not been widespread famine anywhere in the world in the last fifty years in which the local government was not at fault. In Ethiopia in the 1980s, the famous famine was largely caused by the government burning down the fields of those who opposed it. When foreign countries sent food, the government often seized it - an issue in other countries, too. There are still governments which maintain power by controlling the food supply.

That is why the developed nations cannot do much about this issue without going to war, which has its own problems.