When someone's malnourished, they don't get enough to eat. Beyond simply being hungry, someone who's malnourished doesn't get the nutrients they need to be healthy.
Poor countries and those experiencing drought or war are the most likely to have a high percentage of malnourished citizens. If crops can't grow, or food can't be distributed to people who need it, the result is a malnourished population. A malnourished person suffers from malnutrition. Both words use the mal- prefix, meaning "badly," and the Latin root nutrire, "to feed."