Five philosophers are sitting in front of five plates of food, between each plate is one fork. Each philosopher needs to think and eat but to eat they need to hold two forks. Since the forks are shared between two plates a philosopher is only able to grab a fork if it is not already held by another philosopher. After eating for a while the philosophers drops the forks making them available for someone else.
A diagram of the problem shows the five philosophers and the forks (and because I can't do graphics or diagrams my forks looks like diamonds):