Dynamic Programming
Bellman stated the principle of optimality: an optimal solution is made of optimal solutions for the rest of the path.
Why it matters
Sequential decision problems acquired the decomposition that state-value estimation in reinforcement learning is built on.
The book also introduces the phrase curse of dimensionality for the growth of computation with the number of state variables. The Bellman equation later became the basis of temporal-difference methods; Samuel's checkers program used that kind of update, without the name.