Supermassive spoilers - click at your own risk.
Midgardsormr has no relationship to Midgar or the Midgar Zolom in this game, seeing as neither exist. The name is drawn from Norse myth - "Midgar Zolom" is just a bad translation of Midgardsormr.
Midgardsormr is essentially a spirit dragon, a being beyond the cycle of life and death, who serves Hydaelyn as part of a pact he made with her in exchange for sanctuary for his children. He came from a faraway planet, being chased by Omega (a series staple killer robot). You fight Midgardsormr in the "Keeper of the Lake" dungeon because he's annoyed you came to his abode. The magitek robots are there because the Keeper of the Lake is the crashed Garlean flagship Agruis, and Gaius' rogue XIVth Legion maintains a token presence there even after his downfall.
Midgardsormr seals away the Blessing of Light under the grounds that the Ascians are deliberately trying to overwhelm and exhaust its power. This (in story anyway) does diminish the PC's power for a time.
It's unclear if he's stronger than Hydaelyn... but as her servant, if she were able to act freely probably not. He is not a primal, but Hydaelyn is.
Midgardsormr hates Ishgard because they settled on Dravanian (dragon) territory and despite initial conflict were eventually able to forge peace by way of the real Shiva's sacrifice, only for the ancient King Thordan to betray said peace and kill the greatwyrm Ratatoskr to eat her eyes for power, very nearly kill the greatwyrm Nidhogg when he came to avenge her by prising out his eyes, and sending a third greatwyrm Hraesvelgr into a deep depression because of it - and then lying about it all in order to keep Ishgard's socio-political structure advantageous to the upper classes and give the common people cause to fight against the ever-vengeful and still very much alive Nidhogg, who survived by guilting Hraesvelgr into giving him one of his eyes (which contain a dragon's life essence and power, hence why the ancient King Thordan and his Knights Twelve ate Ratatoskr's and stashed away Nidhogg's to use as powerful relics).
Bonus: Midgardsormr is heavily implied to be the template for this game's incarnation of Shinryu, as he is a divine / spirit dragon (the literal translation of "Shinryu") and fought against / was pursued by Omega to Hydaelyn, with Omega and Shinryu being archenemies as a series meta staple.