This setting may vary between models and OS X versions, but I have a setting in System Preferences > Energy Saver > Power Adapter that says "Start up automatically after a power failure"
This can be a great feature and setting. But I have not used it in a few years. My experience with it has been when the power comes back on it goes out briefly a few times before it stays on. The Mac keeps trying to start up. My concern being this could be hard on the drives, or power supply, so I have opted not to use it.
My .02