Typical example: you arrive at a crossroads A where both ways work for you, so you choose the one with less traffic. Then at crossroad B you do the same, and then at C, and finally you arrive at destination D.
However, it turns out the heavy traffic at the other A branch was just for a few miles and then it was actually empty after that --- you took optimum local decisions at each step but since you weren't able to look at the big picture, you didn't actually choose the globally optimal route.
As others have pointed, this is related to the mathematical concepts of local and global maxima: sometimes your optimization algorithm happily stops when it finds a local maximum, ignoring the much better global maximum because it didn't actually traversed the whole search domain.
