The phrase has a figurative meaning; it's not about a physical step but a role or responsibility taken. With the chef absent, the sous chef had to step into the breach and manage the kitchen.
Pro Tip 2/3
Temporary Action
This phrase often implies the action is a temporary solution, not a permanent role change. During the blackout, the security guard stepped into the breach and directed traffic.
Pro Tip 3/3
Emergency Context
It is mostly used in an emergency or when someone is unexpectedly unavailable. When the goalkeeper got injured, a field player had to step into the breach.