The blocks are wedge-shaped, so when you stand on the bridge, the wedges are squeezed into the gap. Provided the side pieces don’t move apart, the bridge stays up.
Forces in action
It's all about the arch shape of a bridge; the arch is a very strong shape. If force is applied from above, the force pressing down spreads along the line of bricks, pushing them together to the take the weight. Applying a force from a different direction has a very different result.
Can you really make a bridge from paper that a car can drive over?
Eggs and Arches
Try crushing an egg by holding it at the top and bottom. Its very hard to do. This is because like arch bridges, eggs spread out forces that are put on them. They are strongest at the top and bottom, if this didn't happen chickens wouldn't be able to sit on them.