Minecraft wiki entry for Command_Block, associated text: If it has been activated,
It checks whether it is in "Conditional" mode and the command block behind it hasn't executed successfully (Behind in the sense of the direction it is facing, not in the sense of which command block chained to it),
If true, it triggers another chain command block it is facing, without executing the command.
If false, it checks whether it has been already executed in this game tick. If false, it executes the command and triggers another chain command block it is facing. If true, it does nothing. That means that chained execution cannot be passed to a command block that has already executed in that game tick (loops execute only once).
If it has not been activated, it triggers the chain command block it is facing to attempt execution.