Minecraft wiki entry for Command_Block, associated text: When it is triggered,
If it has been activated, the chain command block checks whether the command block behind it has executed successfully (if in conditional mode), then it delays.
After a delay, if the condition is met before the delay (if in "Conditional" mode), it executes its command once and triggers the chain command block it is pointing to no matter whether the condition met.
If it has not been activated, it triggers (without delay) the chain command block it is facing to attempt execution.