Short answer
A threshold band tells the strategy not to trade unless the new signal is far enough away from the current position to matter. Instead of resizing for every tiny score drift, the system waits until the signal clears a band that is large enough to justify the cost and operational noise of another rebalance.
That does not create edge by itself. It protects an existing edge from getting spent on noise, fees, and tiny corrective trades that look elegant in a backtest but add little in live operation.