This upgrade is used to guarantee that two or more routers run at the same time. The Sync Upgrade has a tuning value of 0 .. 19 (i.e. 1 less than the base router tick rate of 20). This tuning value can be set by right-clicking/$ the Sync Upgrade to open its GUI, or quickly set to a random value by sneak-right-clicking/$ the upgrade.
Any routers with this upgrade installed, with same the tuning value, and with the same number of Speed Upgrades/$ installed, will always run on the same tick. The actual tuning value doesn't matter; only that the value is consistent across the routers you want to synchronise.
This is particularly useful if you have a group of routers with Extruder Modules/$ installed, and want to ensure all modules extend/retract at exactly the same time.
Advanced notes #1: the Sync Upgrade's tuning value actually specifies precisely when the router will run relative to its tick rate. E.g. routers tick every 20 server ticks by default; a Sync Upgrade with a tuning upgrade of 15 ensures the router always/$ runs 15 ticks after that, and that applies to all/$ routers with a 15-tuned Sync Upgrade. And a 16-tuned Sync Upgrade always runs 1 tick after a 15-tuned Sync Upgrade, at least for routers with the same number of Speed Upgrades/$ installed...