Jax Storm is arguably one of my favourite characters in the book, he's definitely in my top three antagonists and he ain't 2 or 3.
Jax is a Bronzeman first and foremost, and they are very different to mainland Cephri. Mainlanders would think of the Bronzemen as uncivilised, but the Bronzemen see themselves as free - they don't involve themselves in the courtly business of the Seven Kingdoms, they just live amongst themselves and raid areas to the east of Cephri and west of Eilleas. So Jax is unforgiving like his other Bronzemen, he values strength above everything and does not care about meddling about like snakes at court do. Much like the other Bronzemen, Jax is a devout follower of the Drowned God. He follows the religion by dousing his face in saltwater the first thing in the morning - to be reborn. He doesn't fear drowning and he doesn't fear the seas, for they are his God's domain, and when you drown you sink to the floor of the ocean, eventually finding your way to the Drowned God's Palace. Jax pretty much believes in a Darwinian 'survival of the fittest' believing that the Drowned God makes people strong and weak for a reason, he also believes that the Bronzemen need to go back to the 'old way' of reaving and raiding.
Jax's is very strong and admirable in front of his soldiers, he's very prideful but there's a second dynamic when Jax is with his family. His father scolds him for being late but Jax doesn't do anything except stay quiet, although he percieves himself at the top of his hierarchy he obeys his father without fault. Jax tells us his father beat them into submission when his family were children. We see another moment like this during the Battle of King's Landing, where Jax's father doesn't place his ship in the front lines. Jax knows he deserves to be at the front lines but he has to obey his father. When he attempts to give advice to his father on how he would arrange the fleet, his father's 'eyes were unforgiving full of contempt enraged at how his son was questioning him'. He does feel he has something to prove to his father, Jax and his men know how great he is but his father holds him back and Jax believes that in King's Landing he 'will kill all his enemies and prove [himself] worthy'. He feels incensed when his father tells Jax and the second line of ships to stay back while he goes ahead and attacks, he feels ashamed by his father's decision and finally Jax decides to rebel against his father's decisions, but for now he'll obey his father's words. When Jax does rebel against his father he leads his fleet into total failure, it's ironic. He approaches with his fleet but realises that it's too late as Red Fìros explodes in the bay of Redwater and Jax's fleet is totally decimated. The one time he rebelled against his father to prove himself worthy, he failed.
While Jax burns and drowns he fumbles to detach his armour, and although he doesn't think of it - Jax's subconcious is actually afraid of drowning. The whole Red Fìros has sort of uncovered another layer to Jax, he's failed to impress his father by getting his fleet destroyed and he's failed himself and his God by fearing drowning. I think that is one of the most impressive lines in the book.
However, he emerges from the seawater - he doesn't drown. I like to think that Jax Storm, the son of Javon Storm died when he went under, and when he rearose he became Lord Jax Storm of The Bronze Isles(consider that all of Jax's family died in the Red Fìros explosion, now Jax is the only living Storm left). Jax is reborn again from the seawater, gifted life by the Drowned God; him being flinged into the ocean was sort of like a baptism. When he is rescued and put on Lord Harlow's galley, Harlow is afraid of the fire and doesn't want to go - Jax reminds Harlow that he has been 'set on fire'. Jax has become Lord Jax Storm here, he could have stared fear in the face and ran but he has looked at fear and gone to chase after it. Jax is incredibly resilient.
We see his resiliance further in the battle, when the wall of Red Fìros (that Ignis has on the beach) is breached and a hole appears, Jax Storm is the first person through the gap. He fights strongly in the Battle, beating people with ease and he whips Ignis Swyft around in Garibald Shell's Smith. It is only when Jax is distracted does Ignis kill him with a hammer to the head.