Okay, in a nut shell:
Akatosh is depicted in Imperial lore as a dragon. In ancient times, the dragons - of which Akatosh is one - ravaged humans and elves, wreaking havoc the world over. Dragons were very much a destructive, deadly force.
Akatosh made a covenant with St Alessia. The details of that covenant and how it came to be are left somewhat ambiguous, but Alessia's blood was mystically joined with that of the dragons. Akatosh produced the amulet of kings from his own heart, and Alessia led her people out of Skyrim and into Cyrodiil where they became Imperials. The Nords were the humans who remained in Skyrim, rather than becomming Imperials. The two provinces and people have always been closely linked, though. The Nordic interpretation of Akatosh is Alduin, the World Eater. The destroyer of the World.
Akatosh is the god of time, and from the Imperials' point of view, their patron and protector. Alduin is also the god of time, but is the END of time; the force which will devour the world. They can be and very likely are the same being, with two different aspects, each necessary and equally real.
Another aspect of this covenant between man and Akatosh was that Mehrunes Dagon and Oblivion would not be able to enter the mortal world so long as the dragonfires burn, and an heir of the dragon's blood sat upon the throne. That covenant was broken in TES IV, 200 years before Skyrim.
Spoiler Martin's morphing into the avatar of Akatosh did defeat Mehrunes Dagon, but as far as anyone knows before TES V begins, also killed the last of the Dragonborn.
200 years after the events of Oblivion crisis, as far as anyone knows there are no more Dragonborn. You play as the one who is, very possibly, the last in all the world. The dragonfires are gone. There hasn't been a dragonborn on the throne of the mortal world for 200 years. The covenant has been broken. Akatosh/Alduin and the dragons are no longer bound by the ancient treaty, and may now once again ravage the world.
That's my interpretation of the canonical texts in TES. However, there are also texts at the Imperial Library website which go further into the metaphysical aspects of this, which are hotly debated as to whether they constitute canon or not. The reason for the debate is that they do not appear in any of the games, but were written by Bethesda's lore-writers all the same.
One such text speaks of how the world has been created and destroyed many times over. It goes on to say that every time the world is consumed by Akatosh (to be subsequently recreated,) Mehrunes Dagon is always there to try to stop it, and Lorkhan is always trying to hide from Akatosh. Mehrunes Dagon once, many cycles ago, tried to hide a bit of the world each time it was consumed, so that each time it was recreated the world would be a bit larger. His plan was to eventually make the world so large that Akatosh's belly would burst when he ate it. Akatosh discovered this however, and damned Dagon to Oblivion. He could only ever escape Oblivion, if he succesfully destroyed every bit of excess world he created.
One of my theories is that his invasion of Earth was actually an attempt to destroy the excess, and that the modern interpretation of him being responsible for the sphere of destruction is a direct result of his NEED to destroy part of Nirn (Tamriel itself perhaps being the excess?) in order to liberate himself. Likewise, in this interpretation, Akatosh is neither good nor evil. He is simply time itself, and just as time in this universe had a beginning, it must have an end. Akatosh can therefore easily also be Alduin; two faces of the same being; beginning and end, creation and destruction.
You also have to understand that the gods in TES lore can exist in multiple levels, and in varying forms. They can be both a large, primal force such as "time," while also taking a more definite form, such as a dragon, in order to undertake their work.