Synergy is a passive ability of the Advent Beam Defense Platform. Once researched, it stacks with up to five other Beam Defense Platforms to give up to a 50% boost to damage and an undetermined boost to shields. It does not seem to stack up higher than five platforms.
The bonus does not seem to extend to other Beam Cannon armed units in the area, like the Illuminator Vessel or some capital ships. This bonus allows Beam Defense Platforms to be much more effective than they were in pre-Entrenchment Sins, but they are still vulnerable to attack. Don't expect your enhanced Beam Defense Platforms to be able to take on post-Diplomacy pirate raids without support from other defenses (upgraded starbase, repair platforms, hangars) or from the actual fleet.