For example, in chess, if a "node" is considered to be a legal position, the average branching factor has been said to be about 35. This means that, on average, a player has about 35 legal moves at his disposal at each turn. By comparison, the branching factor for the game Go is 250.
Higher branching factors make algorithms that follow every branch at every node, such as exhaustive search, computationally more expensive due to the exponential number of nodes, leading to combinatorail explosion.
For example, if the branching factor is 10, then there will be 10 nodes one level down from the current position, 100 nodes two levels down, 1,000 nodes three levels down, and so on. The higher the branching factor, the faster this "explosion" occurs. The branching factor can be cut down by a pruning algorithm.