A brave Fed Anaconda calls in a Fed Destroyer reinforcement fleet to stop a dastardly Mod Starbridge.
A Reinforcement fleet is a fleet that's called in by the government of a system if their allies are under attack in the system and the combat odds that they face exceed the maximum odds tolerated by that system's government.
The approach of reinforcements will be called out at the bottom of the screen: "Reinforcement fleet of [govt X] detected."
It'll appear in a specified amount of time, usually 60 seconds for remote systems and less for populated systems. After being called, a reinforcement fleet takes time (in days) to replenish, again usually longer for remote systems.
Some systems, like Sol, have powerful Vell-os reinforcement fleets. Sometimes causing a ruckus is the quickest way to meet a telepath.
Given that the pilot takes days to travel through hyperspace, one wonders how reinforcement fleets manage to arrive in mere seconds. The philosophical implications are staggering.