The dining philosophers problem involves 5 philosophers sharing 6 forks placed between them to eat spaghetti. Each philosopher must alternate between thinking and eating, but can only eat when holding both forks to their left and right. The problem is how to design an algorithm such that no philosopher starves while eating and thinking in parallel. The code implements a solution using locks to synchronize access to forks, with each philosopher acquiring left and right forks using locks before eating and releasing after. The output shows the philosophers eating 1 or 2 times each to demonstrate the algorithm working.