A trait is an aspect of a creature, just like in my example, anger is an aspect, fear is an aspect, hatred is an aspect, etc. etc. An aspect is a part of another being.
Alduin is himself an aspect of Akatosh, the aspect of the part of Akatosh, who is time itself, that deals with THE END!
An when regarded to the other Aedra, aspects refer to what part of the TIME DRAGON they are, Akatosh is the mannish aspect of the time dragons, Auri-El is the elves,and Alkosh is the Khajiit aspect. Alduin being an aspect of Akatosh really makes him an aspect of an aspect.
Or in better terms, Alduin isn't a fragment of the TIME DRAGON oversoul, hes a fragment of the fragment of the oversoul that is Akatosh.