What is the meaning of The volunteers were always willing to step into the breach and offer assistance to the tornado victims?

Do I assume correctly that you want to know the meaning of the phrase "step into the breach"? A breach is a break in a wall, dike or similar object. In times gone by, armies faced each other in battle like two walls of soldiers. Because there was no room between the soldiers, the enemy could not outflank them and attack from the side where they were more vulnerable. But if one of the soldiers was killed, there was a gap in the wall of soldiers. Unless this gap were closed up, the enemy would attack the gap and break the defensive wall, defeating them. As soon as a gap or breach occured in the wall, soldiers in reserve standing behind the line would step forward and fill the gap, preventing the enemy from exploiting the weakness. They stepped into the breach.

Stepping into the breach figuratively means stepping forward when you see a need and filling that need. In the example, there was a need for people to assist the tornado victims, and the volunteers saw that need and filled it.