Extra dynamite is a switch that is categorised under the construction patches. It basically allows you to demolish town owned bridges, tunnels and crossroads, things that can not be done otherwise.
In effect, this allowing drag and drop bulldozing over towns with no worry of error messages from crossroads, As in the original game, the crossroads had to have no attaching road before they could be removed. Extra dynamite allows bulldozing them. The patch does not prevent such demolition having a detrimental effect on your ratings with the local authority, so you may still find yourself unable to demolish things if your ratings are very low.
Extra dynamite is also a good way to destroy competitors' routes if they are running on town owned roads